In

physical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

,

**cosmic inflation**,

**cosmological inflation** or just

**inflation** is the theorized extremely rapid

exponentialExponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...

expansionThe metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

of the early

universeThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

by a factor of at least 10

^{78} in volume, driven by a negative-pressure

vacuum energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

density. The

inflationary epochIn physical cosmology the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion...

comprises the first part of the

electroweak epochIn physical cosmology the electroweak epoch was the period in the evolution of the early universe when the temperature of the universe was high enough to merge electromagnetism and the weak interaction into a single electroweak interaction . The electroweak epoch began when the strong force...

following the

grand unification epochIn physical cosmology, assuming that nature is described by a Grand unification theory, the grand unification epoch was the period in the evolution of the early universe following the Planck epoch, starting at about 10−43 seconds after the Big Bang, in which the temperature of the universe was...

. It lasted from 10

^{−36} seconds after the

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

to sometime between 10

^{−33} and 10

^{−32} seconds. Following the inflationary period, the universe continues to expand.

The term "inflation" is also used to refer to the hypothesis that inflation occurred, to the theory of inflation, or to the

inflationary epochIn physical cosmology the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion...

. The inflationary hypothesis was originally proposed in 1980 by American physicist

Alan GuthAlan Harvey Guth is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory...

, who named it "inflation". It was also proposed by Katsuhiko Sato in 1981.

As a direct consequence of this expansion, all of the observable universe originated in a small

causally connectedCausality is the relationship between causes and effects. It is considered to be fundamental to all natural science, especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics....

region. Inflation answers the classic conundrum of the Big Bang cosmology: why does the universe appear flat,

homogeneousIn general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...

and isotropic in accordance with the

cosmological principleIn modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...

when one would expect, on the basis of the physics of the Big Bang, a highly curved, heterogeneous universe? Inflation also explains the origin of the large-scale structure of the cosmos.

Quantum fluctuationIn quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, arising from Werner Heisenberg's uncertainty principle.According to one formulation of the principle,energy and time can be related by the relation...

s in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the universe (see

galaxy formation and evolutionThe study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have generated the variety of structures observed in nearby...

and

structure formationStructure formation refers to a fundamental problem in physical cosmology. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.7 Gyr ago...

).

While the detailed

particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

mechanism responsible for inflation is not known, the basic picture makes a number of predictions that have been confirmed by observation. Inflation is thus now considered part of the standard hot

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

cosmology. The hypothetical

particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

or

fieldIn physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...

thought to be responsible for inflation is called the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

.

## Overview

While

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such constraint in

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. An expanding universe generally has a cosmological horizon, and like a black hole event horizon, this marks the boundary to the part of the universe that an observer can see. The horizon is the boundary beyond which objects are moving away too fast to be visible from Earth.

There are two ways to describe a spacetime with a horizon: global and local. The global picture includes regions beyond the horizon, which are invisible to us, while the local picture is the picture from one point of view only. These two perspectives are related by a process of extension: wherever there is a horizon, a solution of General Relativity can go on by assuming that nothing special happens there. The local and global points of view have a different notion of time. From the local point of view, time stops at the horizon. From the global point of view, time marches on, and surfaces of constant time cross the horizon. Ignoring quantum mechanics, the two pictures are equivalent: any statement can be translated freely back and forth.

For cosmology in the global point of view, the

observable universeIn Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

is one

*causal patch* of a much larger unobservable universe; there are parts of the universe which cannot communicate with us yet. These parts of the universe are outside our current cosmological horizon. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view. As we see these regions for the first time, they look no different from any other region of space we have already seen: they have a background radiation which is at nearly exactly the same temperature as the background radiation of other regions, and their space-time curvature is evolving lock-step with ours. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They couldn't have learned it by getting signals, because they were not in communication with our past light cone before.

Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communications. In the global point of view, the spatial slices are expanding very fast to cover huge volumes. In the local point of view, things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous very quickly.

In either view, as the scalar field slowly relaxes to the vacuum, the cosmological constant goes to zero, and space begins to expand normally. The new regions which come into view during the normal expansion phase, in the global point of view, are exactly the same regions which were pushed out of the horizon during inflation, and so they are necessarily at nearly the same temperature and curvature, because they come from the same little patch of space. In the local point of view, the cosmological horizon still is at the big bang, and inflation is always going on in a thin skin where time is nearly stopped, and the same process produces new regions as it always did, up to small fluctuations.

Inflation from the global point of view is often called eternal inflation. On a global constant-time slice, regions with inflation have an exponentially growing volume, while regions which are not inflating don't. This means that the volume of the inflating part of the universe in the global picture is always unimaginably larger than the part that has stopped inflating. If the probability of different regions is counted by volume, one should expect that inflation will never end, or applying boundary conditions that we exist to observe it, that inflation will end as late as possible. Weighting by volume is unnatural in the local point of view where inflation is not eternal—it eventually ends as seen by any single observer. This picture gives a meaning to the probability distribution on the anthropic landscape, and naively seems more compatible with the

holographic principleThe holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon...

.

The theory of inflation in any picture explains why the temperatures and curvatures of different regions are so nearly equal, and it predicts that the total curvature of a space-slice at constant global time is zero. This prediction means that the total ordinary matter,

dark matterIn astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

, and residual

vacuum energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

in the universe have to add up to the critical density, a prediction which is very accurately confirmed. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and these quantitative predictions have also been confirmed.

### Space expands

To say that space expands exponentially means that two

inertial observerIn physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

s are moving farther apart with accelerating velocity. In stationary coordinates for one observer, a patch of an inflating universe has the following polar

metricIn the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...

:

This is just like an inside-out

black holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

metricIn Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...

—it has a zero in the

component on a fixed radius sphere called the cosmological horizon. Objects are drawn away from the observer at

towards the cosmological horizon, which they cross in a finite proper time. This means that any inhomogeneities are smoothed out, just as any bumps or matter on the surface of a black hole horizon are swallowed and disappear.

Since the space–time metric has no explicit time dependence, once an observer has crossed the cosmological horizon, observers closer in take its place. This process of falling outward and replacement points closer in are always steadily replacing points further out—an exponential expansion of space–time.

This steady-state exponentially expanding spacetime is called a

de Sitter spaceIn mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n-dimensional de Sitter space , denoted dS_n, is the Lorentzian manifold analog of an n-sphere ; it is maximally symmetric, has constant positive curvature,...

, and to sustain it there must be a

cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

, a

vacuum energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

proportional to

everywhere. In this case, the

equation of stateIn cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number \! w, equal to the ratio of its pressure \! p to its energy density \! \rho: \! w=p/\rho...

is

. The physical conditions from one moment to the next are stable: the rate of expansion, called the Hubble parameter, is nearly constant, and the scale factor of the universe is proportional to

. Inflation is often called a period of

*accelerated expansion* because the distance between two fixed observers is increasing exponentially (i.e. at an accelerating rate as they move apart), while

can stay approximately constant (see

deceleration parameter).

### Few inhomogeneities remain

Cosmological inflation has the important effect of smoothing out

inhomogeneitiesIn general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...

,

anisotropiesAnisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...

and the

curvature of spaceThe shape of the universe is a matter of debate in physical cosmology over the local and global geometry of the universe which considers both curvature and topology, though, strictly speaking, it goes beyond both...

. This pushes the universe into a very simple state, in which it is completely dominated by the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

field, the source of the cosmological constant, and the only significant inhomogeneities are the tiny quantum fluctuations in the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

. Inflation also dilutes exotic heavy particles, such as the

magnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

s predicted by many extensions to the

Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

of

particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

. If the universe was only hot enough to form such particles

*before* a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the

observable universeIn Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

. Together, these effects are called the inflationary "no-hair theorem" by analogy with the

no hair theoremThe no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum...

for

black holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s.

The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for philosophical disagreements about what is on the other side. The interpretation of the no-hair theorem is that the universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe,

energy densitiesEnergy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...

generally fall, or get diluted, as the volume of the universe increases. For example, the density of ordinary "cold" matter (dust) goes as the inverse of the volume: when linear dimensions double, the energy density goes down by a factor of eight; the radiation energy density goes down even more rapidly as the universe expands since the wavelength of each photon is stretched (

redshiftIn physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...

ed), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen.

During inflation, the energy density in the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

field is roughly constant. However, the energy density in inhomogeneities, curvature, anisotropies and exotic particles is falling, and through sufficient inflation these become negligible.

This leaves an empty, flat, and symmetric universe, which is filled with radiation when inflation ends.

### Key requirement

A key requirement is that inflation must continue long enough to produce the present observable universe from a single, small inflationary

Hubble volumeIn cosmology, the Hubble volume, or Hubble sphere, is the region of the Universe surrounding an observer beyond which objects recede from the observer at a rate greater than the speed of light, due to the expansion of the Universe....

. This is necessary to ensure that the universe appears flat, homogeneous and isotropic at the largest observable scales. This requirement is generally thought to be satisfied if the universe expanded by a factor of at least 10

^{26} during inflation.

### Reheating

Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model dependent, but in the first models it was typically from 10

^{27}K down to 10

^{22}K.) This relatively low temperature is maintained during the inflationary phase. When inflation ends the temperature returns to the pre-inflationary temperature; this is called

*reheating* or thermalization because the large potential energy of the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

field decays into particles and fills the universe with

Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

particles, including

electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

, starting the

radiation dominated phaseThe radiation-dominated era refers to one of the three phases of the known universe, the other two being the matter-dominated era and the dark-energy-dominated era. During this era, the dynamics of the universe were set by radiation, which refers generally to the constituents of the universe which...

of the Universe. Because the nature of the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

is not known, this process is still poorly understood, although it is believed to take place through a

parametric resonanceA parametric oscillator is a harmonic oscillator whose parameters oscillate in time. For example, a well known parametric oscillator is a child pumping a swing by periodically standing and squatting to increase the size of the swing's oscillations. The varying of the parameters drives the system...

.

## Motivation

Inflation resolves several problems in the

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

cosmology that were pointed out in the 1970s.

Inflation was first discovered by Guth while investigating the problem of why we see no magnetic monopoles today; he found that a positive-energy

false vacuumIn quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles...

would, according to

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, generate an exponential expansion of space. It was very quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does

*today*, the universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.

### Magnetic-monopole problem

The

magnetic-monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

problem (sometimes called the exotic-relics problem) says that if the early universe were very hot, a large number of very heavy, stable

magnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

s would be produced. This is a problem with Grand Unified Theories, which proposes that at high temperatures (such as in the early universe) the electromagnetic force, strong and weak

nuclear forceThe nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...

s are not actually fundamental forces but arise due to

spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....

from a single

gauge theoryIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...

. These theories predict a number of heavy, stable particles that have not yet been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "knot" in the magnetic field. Monopoles are expected to be copiously produced in Grand Unified Theories at high temperature, and they should have persisted to the present day, to such an extent that they would become the primary constituent of the universe. Not only is that not the case, but all searches for them have so far turned out fruitless, placing stringent limits on the density of relic magnetic monopoles in the universe.

A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: monopoles would be separated from each other as the universe around them expands, potentially lowering their observed density by many orders of magnitude. Though, as Martin Rees has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"

### Horizon problem

The

horizon problemThe horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the 1970s. It points out that different regions of the universe have not "contacted" each other because of the great distances between them, but nevertheless they have the same temperature...

is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with the

cosmological principleIn modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...

. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only the

matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

and

radiationIn physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

known in the

Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

—thus have never come in to

causal contactTwo entities are in causal contact if there may be an event that has affected both in a causal way. Every object of mass in space, for instance, exerts a field force on all other objects of mass, according to Newton's law of universal gravitation...

: in the history of the universe, back to the earliest times, it has not been possible to send a light signal between the two regions. Because they have no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). This is because the Hubble radius in a radiation or matter-dominated universe expands much more quickly than physical lengths and so points that are out of communication are coming into communication. Historically, two proposed solutions were the Phoenix universe of

Georges LemaîtreMonsignor Georges Henri Joseph Édouard Lemaître was a Belgian priest, astronomer and professor of physics at the Catholic University of Louvain. He was the first person to propose the theory of the expansion of the Universe, widely misattributed to Edwin Hubble...

and the related oscillatory universe of Richard Chase Tolman, and the

Mixmaster universeThe Mixmaster Universe is a solution to Einstein's field equations of general relativity studied by Charles Misner in an effort to better understand the dynamics of the early universe...

of Charles Misner. Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of

entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the universe

*more* chaotic, could lead to statistical homogeneity and isotropy.

### Flatness problem

Another problem is the

flatness problem (which is sometimes called one of the Dicke coincidences, with the other being the cosmological constant problem). It had been known in the 1960s that the density of matter in the universe was comparable to the critical density necessary for a flat universe (that is, a universe whose large scale

geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

is the usual

Euclidean geometryEuclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

, rather than a

non-EuclideanNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...

hyperbolicIn mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...

or

spherical geometrySpherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry which is not Euclidean. Two practical applications of the principles of spherical geometry are to navigation and astronomy....

).

Therefore, regardless of the

shape of the universeThe shape of the universe is a matter of debate in physical cosmology over the local and global geometry of the universe which considers both curvature and topology, though, strictly speaking, it goes beyond both...

the contribution of spatial curvature to the expansion of the universe could not be much greater than the contribution of matter. But as the universe expands, the curvature

redshiftIn physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...

s away more slowly than matter and radiation. Extrapolated into the past, this presents a

fine-tuningIn theoretical physics, fine-tuning refers to circumstances when the parameters of a model must be adjusted very precisely in order to agree with observations. Theories requiring fine-tuning are regarded as problematic in the absence of a known mechanism to explain why the parameters happen to...

problem because the contribution of curvature to the universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at

big bang nucleosynthesisIn physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...

, for example). This problem is exacerbated by recent observations of the cosmic microwave background that have demonstrated that the universe is flat to the accuracy of a few percent.

### Precursors

In the early days of

General RelativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

,

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

introduced the

cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

to allow a static solution which was a three dimensional sphere with a uniform density of matter. A little later,

Willem de SitterWillem de Sitter was a Dutch mathematician, physicist and astronomer.-Life and work:Born in Sneek, De Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. He worked at the Cape Observatory in South Africa...

found a highly symmetric inflating universe, which described a universe with a cosmological constant which is otherwise empty. It was discovered that Einstein's solution is unstable, and if there are small fluctuations, it eventually turns into de Sitter's.

In the early 1970s Zeldovich noticed the serious flatness and horizon problems of big bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds. In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic

BKL singularityA BKL singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by an anisotropic, homogeneous, chaotic solution to Einstein's field equations of gravitation...

in General Relativity. Misner's

Mixmaster universeThe Mixmaster Universe is a solution to Einstein's field equations of general relativity studied by Charles Misner in an effort to better understand the dynamics of the early universe...

attempted to use this chaotic behavior to solve the cosmological problems, with limited success.

In the late 1970s,

Sidney ColemanSidney Richard Coleman was an American theoretical physicist who studied under Murray Gell-Mann.- Life and work :Sidney Coleman grew up on the Far North Side of Chicago...

applied the

instantonAn instanton is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory...

techniques developed by Alexander Polyakov and collaborators to study the fate of the

false vacuumIn quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles...

in quantum field theory. Like a metastable phase in statistical mechanics—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.

In the Soviet Union, Starobinsky noted that quantum corrections to general relativity should be important in the early universe, and these generically lead to curvature-squared corrections to the Einstein–Hilbert action. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, can lead to an effective cosmological constant, so he proposed that the early universe went through a deSitter phase, an inflationary era. This resolved the problems of cosmology, and led to specific predictions for the corrections to the microwave background radiation, corrections which were calculated in detail shortly afterwards.

In 1978, Zeldovich noted the monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a fashionable subfield of particle physics, which led to several speculative attempts to resolve it. In 1980, working in the west,

Alan GuthAlan Harvey Guth is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory...

realized that false vacuum decay in the early universe would solve the problem, leading him to propose scalar driven inflation. Starobinski's and Guth's scenarios both predicted an initial deSitter phase, differing only in the details of the mechanism.

### Early inflationary models

Inflation was proposed in January, 1980 by

Alan GuthAlan Harvey Guth is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory...

as a mechanism for resolving these problems. At the same time, Alexei Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the universe with an exponentially expanding deSitter phase. In October 1980 Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem, and Sato suggesting that an exponential expansion could eliminate

domain wallA domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...

s (another kind of exotic relic.) In 1981 Einhorn and Sato published a model similar to Guth's and showed that it would resolve the puzzle of the

magnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would very likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.

Guth proposed that as the early universe cooled, it was trapped in a

false vacuumIn quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles...

with a high energy density, which is much like a

cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

. As the very early universe cooled it was trapped in a

metastableMetastability describes the extended duration of certain equilibria acquired by complex systems when leaving their most stable state after an external action....

state (it was

supercooledSupercooling, also known as undercooling, is the process of lowering the temperature of a liquid or a gas below its freezing point without it becoming a solid....

) which it could only decay out of through the process of

bubble nucleationNucleation is the extremely localized budding of a distinct thermodynamic phase. Some examples of phases that may form by way of nucleation in liquids are gaseous bubbles, crystals or glassy regions. Creation of liquid droplets in saturated vapor is also characterized by nucleation...

via quantum tunneling. Bubbles of

true vacuumIn quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...

spontaneously form in the sea of false vacuum and rapidly begin expanding at the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble will nucleate.

### Slow-roll inflation

The bubble collision problem was solved by

Andrei LindeAndrei Dmitriyevich Linde is a Russian-American theoretical physicist and professor of Physics at Stanford University. Dr. Linde is best known for his work on the concept of the inflationary universe. He received his Bachelor of Science degree from Moscow State University. In 1975, Linde was...

and independently by

Andreas AlbrechtAndreas Albrecht is a cosmologist involved in research and teaching in the University of California, Davis. Along with João Magueijo, Andreas Albrecht independently proposed a model of varying speed of light cosmology...

and

Paul SteinhardtPaul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...

in a model named

*new inflation* or

*slow-roll inflation* (Guth's model then became known as

*old inflation*). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a

scalar fieldIn mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur.

### Effects of asymmetries

Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that tiny quantum fluctuations in the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

are created. These tiny fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in the

Soviet UnionThe Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....

in analyzing Starobinsky's similar model. In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at

Cambridge UniversityThe University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

. The fluctuations were calculated by four groups working separately over the course of the workshop:

Stephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

; Starobinsky; Guth and So-Young Pi; and

James M. BardeenJames Maxwell Bardeen is an American physicist, well known for his work in general relativity, particularly his role in formulating the laws of black hole mechanics. He also discovered the Bardeen vacuum, an exact solution of the Einstein field equation.Bardeen graduated from Harvard in 1960 and...

,

Paul SteinhardtPaul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...

and

Michael TurnerMichael S. Turner is a theoretical cosmologist, who coined the term dark energy.He is the Bruce V. & Diana M. Rauner Distinguished Service Professor at the University of Chicago, and was formerly the Assistant Director for Mathematical and Physical Sciences for the US National Science Foundation...

.

## Observational status

Inflation is a concrete mechanism for realizing the

cosmological principleIn modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...

which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the

Wilkinson Microwave Anisotropy ProbeThe Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...

(WMAP) spacecraft. This analysis shows that the universe is flat to an accuracy of at least a few percent, and that it is homogeneous and isotropic to a part in 10,000.

In addition, inflation predicts that the structures visible in the universe today formed through the

gravitational collapseGravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...

of perturbations which were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations called a nearly-scale-invariant

Gaussian random fieldA Gaussian random field is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is also called a Gaussian process....

(or Harrison-Zel'dovich spectrum) is very specific and has only two free parameters, the amplitude of the spectrum and the

*spectral index* which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe). Inflation predicts that the observed perturbations should be in

thermal equilibriumThermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

with each other (these are called

*adiabatic* or

*isentropic* perturbations). This structure for the perturbations has been confirmed by the WMAP spacecraft and other cosmic microwave background experiments, and galaxy surveys, especially the ongoing

Sloan Digital Sky SurveyThe Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project was named after the Alfred P...

. These experiments have shown that the one part in 10,000 inhomogeneities observed have exactly the form predicted by theory. Moreover, there is evidence for a slight deviation from scale invariance. The

*spectral index*,

*n*_{s} is equal to one for a scale-invariant spectrum. The simplest models of inflation predict that this quantity is between 0.92 and 0.98. From the data taken by the WMAP spacecraft it can be inferred that

*n*_{s} = 0.963 ± 0.012, implying that it differs from one at the level of two

standard deviationStandard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

s (2σ). This is considered an important confirmation of the theory of inflation.

A number of theories of inflation have been proposed that make radically different predictions, but they generally have much more

fine tuningIn theoretical physics, fine-tuning refers to circumstances when the parameters of a model must be adjusted very precisely in order to agree with observations. Theories requiring fine-tuning are regarded as problematic in the absence of a known mechanism to explain why the parameters happen to...

than is necessary. As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics.

Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature. However, the third-year data revealed that the effect was a statistical anomaly. Another effect has been remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer: the amplitude of the quadrupole moment of the cosmic microwave background is unexpectedly low and the other low multipoles appear to be preferentially aligned with the

ecliptic planeThe plane of the ecliptic is the plane of the Earth's orbit around the Sun. It is the primary reference plane when describing the position of bodies in the Solar System, with celestial latitude being measured relative to the ecliptic plane. In the course of a year, the Sun's apparent path through...

. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to other new physics, foreground contamination, or even

publication biasPublication bias is the tendency of researchers, editors, and pharmaceutical companies to handle the reporting of experimental results that are positive differently from results that are negative or inconclusive, leading to bias in the overall published literature...

.

An experimental program is underway to further test inflation with more precise measurements of the cosmic microwave background. In particular, high precision measurements of the so-called "B-modes" of the polarization of the background radiation will be evidence of the gravitational radiation produced by inflation, and they will also show whether the energy scale of inflation predicted by the simplest models (10

^{15}–10

^{16} GeVGEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...

) is correct. These measurements are expected to be performed by the Planck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere with these measurements. Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars turned on), may measure the power spectrum with even greater resolution than the cosmic microwave background and galaxy surveys, although it is not known if these measurements will be possible or if interference with

radio sourcesRadio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

on earth and in the galaxy will be too great.

Dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

is broadly similar to inflation, and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, 10

^{−12} GeV, roughly 27 orders of magnitude less than the scale of inflation.

## Theoretical status

In the early proposal of Guth, it was thought that the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

was the Higgs field, the field which explains the mass of the elementary particles. It is now known that the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

cannot be the Higgs field. Other models of inflation relied on the properties of grand unified theories. Since the simplest models of grand unification have failed, it is now thought by many physicists that inflation will be included in a supersymmetric theory like

string theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

or a supersymmetric grand unified theory. A promising suggestion is brane inflation. At present, however, while inflation is understood principally by its detailed predictions of the initial conditions for the hot early universe, the particle physics is largely

*ad hoc* modelling. As such, though predictions of inflation have been consistent with the results of observational tests, there are many open questions about the theory.

### Fine-tuning problem

One of the most severe challenges for inflation arises from the need for

fine tuningFine Tuning was the name of XM Satellite Radio's eclectic music channel. The program director for Fine Tuning was Ben Smith and the tag line was, "The World's Most Interesting Music"....

in inflationary theories. In new inflation, the

*slow-roll conditions* must be satisfied for inflation to occur. The slow-roll conditions say that the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

potentialA scalar potential is a fundamental concept in vector analysis and physics . The scalar potential is an example of a scalar field...

must be flat (compared to the large

vacuum energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

) and that the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

particles must have a small mass. In order for the new inflation theory of Linde, Albrecht and Steinhardt to be successful, therefore, it seemed that the universe must have a scalar field with an especially flat potential and special initial conditions.

#### Andrei Linde

Andrei Linde proposed a theory known as

*chaotic inflation*The Chaotic Inflation theory is a variety of the inflationary universe model, which is itself an outgrowth of the Big Bang theory. Chaotic Inflation, proposed by physicist Andrei Linde, models our universe as one of many that grew as part of a multiverse owing to a vacuum that had not decayed to...

in which he suggested that the conditions for inflation are actually satisfied quite generically and inflation will occur in virtually any universe that begins in a chaotic, high energy state and has a scalar field with unbounded potential energy. However, in his model the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

field necessarily takes values larger than one Planck unit: for this reason, these are often called

*large field* models and the competing new inflation models are called

*small field* models. In this situation, the predictions of

effective field theoryIn physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...

are thought to be invalid, as

renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

should cause large corrections that could prevent inflation. This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models of inflation. While inflation depends on quantum field theory (and the

semiclassical approximationSemiclassical gravity is the approximation to the theory of quantum gravity in which one treats matter fields as being quantum and the gravitational field as being classical....

to

quantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

) in an important way, it has not been completely reconciled with these theories.

Robert Brandenberger has commented on fine-tuning in another situation. The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. There are strong suggestions that this scale is around 10

^{16} GeVGEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...

or 10

^{−3} times the

Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a

hierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...

): the energy density given by the scalar potential is down by 10

^{−12} compared to the

Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.

### Eternal inflation

Cosmological inflation seems to be eternal the way it is theorised. Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes bring it back up to previous levels. These regions in which the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

fluctuates upwards expand much faster than regions in which the

inflatonThe inflaton is the generic name of the hypothetical and hitherto unidentified scalar field that may be responsible for the hypothetical inflation in the very early universe...

has a lower potential energy, and tend to dominate in terms of physical volume. This steady state, which first developed by Vilenkin, is called "eternal inflation". It has been shown that any inflationary theory with an unbounded potential is eternal. It is a popular belief among physicists that this steady state cannot continue forever into the past. The inflationary spacetime, which is similar to

de Sitter spaceIn mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n-dimensional de Sitter space , denoted dS_n, is the Lorentzian manifold analog of an n-sphere ; it is maximally symmetric, has constant positive curvature,...

, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space will collapse to form a

gravitational singularityA gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

, a point where densities become infinite. Therefore, it is necessary to have a theory for the universe's initial conditions. Linde, however, believes inflation may be past eternal.

### Initial conditions

Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin. These models propose that while the universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever.

Other proposals attempt to describe the ex nihilo creation of the universe based on

quantum cosmologyIn theoretical physics, quantum cosmology is a field attempting to study the effect of quantum mechanics on the formation of the universe, or its early evolution, especially just after the Big Bang...

and the following inflation. Vilenkin put forth one such scenario. Hartle and Hawking offered the no-boundary proposal for the initial creation of the universe in which inflation comes about naturally.

Alan GuthAlan Harvey Guth is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory...

has described the inflationary universe as the "ultimate free lunch": new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the

first law of thermodynamicsThe first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

(

energy conservationEnergy conservation refers to efforts made to reduce energy consumption. Energy conservation can be achieved through increased efficient energy use, in conjunction with decreased energy consumption and/or reduced consumption from conventional energy sources...

) and the

second law of thermodynamicsThe second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

(

entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

and the

arrow of timeThe arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...

problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the universe came about by a quantum fluctuation. Donald Page was an outspoken critic of inflation because of this anomaly. He stressed that the thermodynamic

arrow of timeThe arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...

necessitates low

entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory further aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.

Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle-Hawking initial state. Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the universe. However, Albrecht and Lorenzo Sorbo have argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state,

*compared* with a non-inflationary cosmos overwhelmingly favours the inflationary scenario, simply because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than any required for a non-inflationary alternative, which outweighs any entropic considerations.

Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects. Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations which have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. There has been some disagreement about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.

### Hybrid inflation

Another kind of inflation, called

*hybrid inflation*, is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.

In hybrid inflation, one of the scalar fields is responsible for most of the energy density (thus determining the rate of expansion), while the other is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.

### Inflation and string cosmology

The discovery of flux compactifications have opened the way for reconciling inflation and string theory. A new theory, called brane inflation suggests that inflation arises from the motion of

D-braneIn string theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava in 1989...

s in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac-Born-Infeld action, is very different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.

### Inflation and loop quantum gravity

When investigating the effects the theory of

loop quantum gravityLoop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

would have on cosmology, a

loop quantum cosmologyLoop quantum cosmology is a finite, symmetry-reduced model of loop quantum gravity that predicts a quantum bridge between contracting and expanding cosmological branches...

model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.

### Criticisms

Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, several physicists, mathematicians and philosophers of science have voiced criticisms, claiming unfulfilled promises and lack of serious empirical support. In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding that “we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology”. Since 1999 the results of the WMAP mission in 2006 made the empirical case for cosmic inflation very compelling.

In order to work, and as pointed out by

Roger PenroseSir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...

from 1986 on, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudoproblem) of initial conditions is not solved: “There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. […] For, if the thermalization is actually doing anything […] then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after.” The problem of specific or “fine-tuned” initial conditions would not have been solved; it would have got worse.

A recurrent criticism of inflation is that the invoked inflation field does not correspond to any known physical field, and that its

potential energyIn physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

curve seems to be an ad hoc contrivance to accommodate almost any data we could get. It is significant that Paul J. Steinhardt, one of the founding fathers of inflationary cosmology, has recently become one of its sharpest critics. He calls ‘bad inflation’ a period of accelerated expansion whose outcome conflicts with observations, and ‘good inflation’ one compatible with them: “Not only is bad inflation more likely than good inflation, but no inflation is more likely than either. … Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation … Other configurations lead to a uniform, flat universe directly –without inflation. Obtaining a flat universe is unlikely overall. Penrose’s shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation –by a factor of 10 to the googol (10 to the 100) power!”

## Adjuncts to inflation

There are models that explain some of the observations explained by inflation. However none of these "alternatives" has the same breadth of explanation as inflation, and still require inflation for a more complete fit with observation; they should therefore be regarded as adjuncts to inflation, rather than as alternatives.

String theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

requires that, in addition to the three spatial dimensions we observe, there exist additional dimensions that are curled up or

compactifiedIn physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic....

(see also Kaluza-Klein theory). Extra dimensions appear as a frequent component of

supergravityIn theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...

models and other approaches to

quantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

. This raises the question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and

Cumrun VafaCumrun Vafa is an Iranian-American leading string theorist from Harvard University where he started as a Harvard Junior Fellow. He is a recipient of the 2008 Dirac Medal.-Birth and education:...

. This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

can only expand if the strings that wind around it can efficiently annihilate each other. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will

generically intersectIn mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology...

(and, presumably, annihilate) is three. Therefore, one argues that the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. For a recent review, see The authors admits that their model "does not solve the entropy and flatness problems of standard cosmology ..... and we can provide no explanation for why the current universe is so close to being spatially flat."

The

ekpyroticThe ekpyrotic universe, or ekpyrotic scenario, is a cosmological model of the origin and shape of the universe. The name comes from a Stoic term ekpyrosis meaning conflagration or in Stoic usage "conversion into fire"...

and

cyclic modelA cyclic model is any of several cosmological models in which the universe follows infinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a...

s are also considered adjuncts to inflation. These models solve the

horizon problemThe horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the 1970s. It points out that different regions of the universe have not "contacted" each other because of the great distances between them, but nevertheless they have the same temperature...

through an expanding epoch well

*before* the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a

Big CrunchIn physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe recollapses, ultimately ending as a black hole singularity.- Overview :...

. The universe passes through the Big Crunch and emerges in a hot

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

phase. In this sense they are reminiscent of the oscillatory universe proposed by Richard Chace Tolman: however in Tolman's model the total age of the universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. They also provide no explanation of the

magnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

problem. Unfortunately, as things stand - there is no evidence of any 'slowing down' of the expansion.

Another adjunct, the varying speed of light model has also been theorized by

Jean-Pierre PetitJean-Pierre Petit is a French scientist, senior researcher at National Center for Scientific Research as an astrophysicist in Marseille Observatory, now retired...

in 1988,

John MoffatJohn W. Moffat is a Professor Emeritus in physics at the University of Toronto.He is also an adjunct Professor in physics at the University of Waterloo and a resident affiliate member of the Perimeter Institute for Theoretical Physics....

in 1992 as well

Andreas AlbrechtAndreas Albrecht is a cosmologist involved in research and teaching in the University of California, Davis. Along with João Magueijo, Andreas Albrecht independently proposed a model of varying speed of light cosmology...

and

João MagueijoJoão Magueijo is a Portuguese cosmologist and professor in Theoretical Physics at Imperial College London. He is a pioneer of the varying speed of light theory.- Career :...

in 1999, instead of superluminal expansion the speed of light was 60 orders of magnitude faster than its current value solving the horizon and homogeneity problems in the early universe.

## See also

- Brane cosmology
Brane cosmology refers to several theories in particle physics and cosmology motivated by, but not exclusively derived from, superstring theory and M-theory.-Brane and bulk:...

- Varying speed of light
- Dark flow
Dark flow is an astrophysical term describing a peculiar velocity of galaxy clusters. The actual measured velocity is the sum of the velocity predicted by Hubble's Law plus a small and unexplained velocity flowing in a common direction....

- Non-minimally coupled inflation
- doughnut theory of the universe
The doughnut theory of the universe is an informal description of the theory that the shape of the universe is a three-dimensional torus. The name comes from the shape of a doughnut, whose surface has the topology of a two-dimensional torus....

## External links