Structure formation refers to a fundamental problem in
physical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of our universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause....
. The
universeThe Universe comprises everything that physically exists, the entirety of space and time, all forms of matter and energy, and the physical laws and constants that govern them...
, as is now known from observations of the
cosmic microwave background radiationIn cosmology, cosmic microwave background radiation is a form of electromagnetic radiation filling the universe. With a traditional optical telescope, the space between stars and galaxies is pitch black...
, began in a hot, dense, nearly uniform state approximately
13.7 Gyr agoThe age of the universe is the time elapsed between the Big Bang and the present day. Current theory and observations suggest that the universe is between 13.5 and 14 billion years old. The uncertainty range has been obtained by the agreement of a number of scientific research projects...
. However, looking in the sky today, we see structures on all scales, from
starA star is a massive, luminous ball of plasma that is held together by gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth. Other stars are visible in the night sky, when they are not outshone by the Sun...
s and
planetA planet , is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
s to
galaxiesA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The name is from the Greek root galaxias [γαλαξίας], meaning "milky," a reference...
and, on much larger scales still, galaxy clusters, and enormous voids between galaxies. How did all of this come about from the nearly uniform early universe?
Overview
Under present models, the structure of the visible universe was formed in the following stages:
- The very early universe In this stage, some mechanism, such as cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10
−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density...
is responsible for establishing the initial conditions of the universe: homogeneity, isotropy and flatness.
- The primordial plasma The universe is dominated by radiation for most of this stage, and due to free streaming
In astronomy, free streaming is a term used to describe a particle, most often a photon, which propagates through a medium without scattering.-Use in defining surfaces:...
structures cannot be amplified gravitationally. Nonetheless, important evolution takes place, such as 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...
creates the primordial elements and the cosmic microwave background is emitted. The detailed anisotropy structure of the cosmic microwave background is also created in this epoch.
- Linear growth of structure Once matter, in particular cold dark matter
In astronomy and cosmology, dark matter is hypothetical matter that is undetectable by its emitted radiation, but whose presence can be inferred from gravitational effects on visible matter...
, dominates the universe gravitational collapse can start to amplify the tiny inhomogeneities left by cosmic inflation, causing matter to fall towards dense regions and making rarefied regions more rarefied. In this epoch, the density inhomogeneities are described by a simple linear differential equationIn mathematics, a linear differential equation is of the formwhere the differential operator L is a linear operator, y is the unknown function , and the right hand side ƒ is a given function of the same nature as y...
.
- Nonlinear growth of structure As the dense regions become denser, the linear approximation describing density inhomogeneities begins to break down – adjacent particles may even begin to cross in caustics
In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. Caustic can also refer to the curve to which light rays are tangent, defining a boundary of an envelope of...
– and a more detailed treatment, using the full Newtonian theory of gravity, becomes necessary. (Aside from the background expansion of the universe, which is due to general relativity, evolution on these comparatively small scales is usually well approximated by the Newtonian theory.) This is where structures, such as galaxy clusters and galaxy haloes begin to form. Still, in this regime only gravitational forces are significant because dark matter, which is thought to have very weak interactions, is the dominant player.
- "Gastrophysical" evolution The final step of the evolution is when electromagnetic forces become important in the evolution of structure, where baryon
Baryons are the family of composite particles made of three quarks, as opposed to the mesons which are the family of composite particles made of one quark and one antiquark. Both baryons and mesons are part of the larger particle family comprising all particles made of quarks—the hadrons...
ic matter clusters densely, as in galaxiesA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The name is from the Greek root galaxias [γαλαξίας], meaning "milky," a reference...
and starA star is a massive, luminous ball of plasma that is held together by gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth. Other stars are visible in the night sky, when they are not outshone by the Sun...
s. In some cases, such as active galactic nucleiAn active galactic nucleus is a compact region at the centre of a galaxy which has a much higher than normal luminosity over some or all of the electromagnetic spectrum . A galaxy hosting an AGN is called an active galaxy...
and quasarA quasi-stellar radio source is a powerfully energetic and distant galaxy with an active galactic nucleus. Quasars were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than extended...
s, Newtonian theory works poorly and general relativity becomes significant. It is called "gastrophysical" because of its complexity: many different, complicated effects, including gravity, magnetohydrodynamicsMagnetohydrodynamics is the academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, and hydro- meaning liquid, and...
and nuclear reactionIn nuclear physics and nuclear chemistry, a nuclear reaction is the process in which two nuclei or nuclear particles collide to produce products different from the initial particles...
s must be taken into account.
The last three stages of evolution occur at different times depending on the scale. The largest scales in the universe are still well-approximated by linear theory, whereas galaxy clusters and superclusters are nonlinear, and many phenomena in the local galaxy must be modelled by a more nuanced approach, accounting for all the forces. This is what is called hierarchical structure formation: the smallest gravitationally bound structures – quasars and galaxies – form first, followed by
groups, clustersGalaxy groups and clusters are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation. They form the densest part of the large scale structure of the universe...
and superclusters of galaxies. It is thought that, because of the presence of
dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. Dark energy is the most popular way to explain recent observations that the universe appears to be...
in our universe, no larger structures will be able to form.
Very early universe
The very early universe is still a poorly-understood epoch, from the viewpoint of fundamental physics. The prevailing theory,
cosmic inflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10
−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density...
, does a good job explaining the observed flatness, homogeneity and isotropy of the universe, as well as the absence of exotic relic particles (such as
magnetic monopoleIn physics, a magnetic monopole is a hypothetical particle that is a magnet with only one pole . In more technical terms, it would have a net "magnetic charge"...
s). In addition, it has made a crucial prediction that has been borne out by observation: that the primordial universe would have tiny perturbations which seed the formation of structure in the later universe. These fluctuations, while they form the foundation for all structure in the universe, appear most clearly as tiny
temperatureIn physics, temperature is a physical property of a system that underlies the common notions of hot and cold; something that feels hotter generally has the higher temperature. Temperature is one of the principal parameters of thermodynamics...
fluctuations at one part in 100,000. (To put this in perspective, the same level of fluctuations on a
topographic mapA topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods...
of the United States would show no feature higher than a few meters high.) These fluctuations are critical, because they provide the seeds from which the largest structures within the universe can grow and eventually collapse to form galaxies and stars.
COBEThe Cosmic Background Explorer , also referred to as Explorer 66, was a satellite dedicated to cosmology. Its goals were to investigate the cosmic microwave background radiation of the universe and provide measurements that would help shape our understanding of the cosmos.This work provided...
(Cosmic Background Explorer) provided the first detection of the intrinsic fluctuations in the cosmic microwave background radiation in the 1990s.
These perturbations are thought to have a very specific character: they form a
Gaussian random fieldA Gaussian random field is a random field involving Gaussian probability density functions of the variables. The initial conditions of physical cosmology generated by quantum mechanical fluctuations during cosmic inflation are thought to be a Gaussian random field with a nearly scale invariant...
whose covariance function is diagonal and nearly scale-invariant. The observed fluctuations appear to have exactly this form, and in addition the
spectral index measured by WMAP – the spectral index measures the deviation from a scale-invariant (or Harrison-Zel'dovich) spectrum – is very nearly the value predicted by the simplest and most robust models of inflation. Another important property of the primordial perturbations, that they are adiabatic (or isentropic between the various kinds of matter that compose the universe), is predicted by cosmic inflation and has been confirmed by observations.
Other theories of the very early universe, which are claimed to make very similar predictions, have been proposed, such as the brane gas cosmology,
cyclic modelA cyclic model is any of several cosmological models in which the universe follows infinite, self-sustaining cycles .-Overview:...
, pre-big bang model and holographic universe, but they remain in their nascency and are not as widely accepted. Some theories, such as
cosmic stringA cosmic string is a hypothetical 1-dimensional topological defect in various fields. Cosmic strings are hypothesized to form when the field undergoes a phase change in different regions of spacetime, resulting in condensations of energy density at the boundaries between regions...
s have largely been falsified by increasingly precise data.
The horizon problem
An extremely important concept in the theory of structure formation is the notion of the Hubble radius, often called simply the
horizon as it is closely related to the
particle horizonIn physical cosmology, particle horizon is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the portion of the universe which we could have conceivably observed at the present day...
. The Hubble radius, which is related to the Hubble parameter as , where is the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
, defines, roughly speaking, the volume of the nearby universe that has recently (in the last expansion time) been in
causalCausality describes the relationship between causes and effects, is fundamental to all natural science, especially physics, and has a basis in logic. It is also studied from the perspectives of philosophy, computer science, and statistics. In physics it is useful to interpret certain terms of a...
contact with an observer. Since the universe is continually expanding, its energy density is continually decreasing (in the absence of truly exotic matter such as
phantom energyPhantom energy is a hypothetical form of dark energy with equation of state . If it exists, it could cause the expansion of the universe to accelerate so quickly that the Big Rip would occur....
). The Friedmann equation relates the energy density of the universe to the Hubble parameter, and shows that the Hubble radius is continually increasing.
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 due to the great distances between them, but nevertheless they have the same temperature and...
of the big bang cosmology says that, without inflation, perturbations were never in causal contact before they entered the horizon and thus the homogeneity and isotropy of, for example, the large scale galaxy distributions cannot be explained. This is because, in an ordinary Friedmann-Robertson-Walker cosmology, the Hubble radius increases more rapidly than space expands, so perturbations are only ever entering the Hubble radius, and they are not being pushed out by the expansion of space. This paradox is resolved by cosmic inflation, which suggests that there was a phase of very rapid expansion in the early universe in which the Hubble radius was very nearly constant. Thus, the large scale isotropy that we see today is due to quantum fluctuations produced during cosmic inflation being pushed outside the horizon.
Primordial plasma
The end of inflation is called reheating, when the inflation particles decay into a hot, thermal plasma of other particles. In this epoch, the energy content of the universe is entirely radiation, with standard model particles having relativistic velocities. As the plasma cools,
baryogenesisIn physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories —...
and
leptogenesis*In physics, leptogenesis is the process of creating a lepton-antilepton asymmetry in the early stages of the universe.*In biblical studies, leptogenesis is an alternative name for book of Jubilees....
are thought to occur, as the
quark-gluon plasmaA quark–gluon plasma is a phase of quantum chromodynamics which exists at extremely high temperature and/or density. This phase consists of free quarks and gluons, which are the basic building blocks of matter...
cools, electroweak symmetry breaking occurs and the universe becomes principally composed of ordinary
protonThe proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H
+...
s,
neutronThe neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutron are usually found in atomic nuclei. The nuclei of most atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of protons in a...
s and
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
s. As the universe cools further,
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...
occurs and small quantities of
deuteriumDeuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in of hydrogen...
,
heliumHelium is the chemical element with atomic number 2, and is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert monatomic gas that heads the noble gas group in the periodic table...
and
lithiumLithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number three. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...
nucleiThe nucleus is the very dense region consisting of nucleons at the center of an atom. Almost all of the mass in an atom is made up from the protons and neutrons in the nucleus, with a very small contribution from the orbiting electrons....
are created. As the universe cools and expands, the energy in photons begins to redshift away, particles become non-relativistic and ordinary matter begins to dominate the universe. Eventually, atoms begin to form as free electrons bind to nuclei. This suppresses Thompson scattering of photons. Combined with the rarefaction of the universe (and consequent increase in the
mean free pathIn physics the mean free path of a particle is the average distance covered by a particle between successive impacts.. Alternatively, it is the distance at which the intensity of particles drops by 1/e.-Derivation:...
of photons), this makes the universe transparent and the cosmic microwave background is emitted at recombination (the
surface of last scattering).
Acoustic oscillations
The amplitude of structures does not grow substantially during this epoch. For dark matter the expansion of space (which is caused by the large radiation component) is so rapid that growth is highly suppressed for the non-relativistic dark matter particles. Moreover, because dark matter is pressureless, free-streaming prevents the growth of small structures. In the relativistic fluid, on the other hand, the very large pressure prevents the growth of structures larger than the
Jeans lengthJeans' length is the critical radius of a cloud where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse...
, which is very nearly equal to the Hubble radius for radiation. This causes perturbations to be damped.
These perturbations are still very important, however, as they are responsible for the subtle physics that result in the cosmic microwave background anisotropy. In this epoch, the amplitude of perturbations which enter the horizon oscillate sinusoidally, with dense regions becoming more rarefied and then becoming dense again, with a frequency which is related to the size of the perturbation. If the perturbation oscillates an integral or half-integral number of times between coming into the horizon and recombination, it appears as an acoustic peak of the cosmic microwave background anisotropy. (A half-oscillation, in which a dense region becomes a rarefied region or vice-versa, appears as a peak because the anisotropy is displayed as a
power spectrum, so underdensities contribute to the power just as much as overdensities.) The physics which determines the detailed peak structure of the microwave background is complicated, but these oscillations provide the essence.
Linear structure
One of the key realizations made by cosmologists in the 1970s and 1980s was that the majority of the
matterThe term matter traditionally refers to the substance that all objects are made of. One common way to identify this "substance" is through its physical properties; a common definition of matter is anything that has mass and occupies a volume...
content of the universe was composed not of atoms, but rather a mysterious form of matter known as dark matter. Dark matter interacts through the force of gravity, but it is not composed of
baryonBaryons are the family of composite particles made of three quarks, as opposed to the mesons which are the family of composite particles made of one quark and one antiquark. Both baryons and mesons are part of the larger particle family comprising all particles made of quarks—the hadrons...
s and it is known with very high accuracy that it does not emit or absorb
radiationIn physics, radiation describes any process in which energy emitted by one body travels through a medium or through space, ultimately to be absorbed by another body...
. It may be composed of particles that interact through the
weak interactionThe weak interaction is one of the four fundamental interactions of nature. In the Standard Model of particle physics, it is due to the exchange of the heavy W and Z bosons...
, such as
neutrinoNeutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero mass...
s, but it cannot be composed entirely of the three known kinds of neutrinos (although some have suggested it is a
sterile neutrinoA sterile neutrino is a hypothetical neutrino that does not interact via any of the fundamental interactions of the Standard Model except gravity[Real neutral particle]...
). Recent evidence suggests that there is about five times as much dark matter as baryonic matter, and thus the dynamics of the universe in this epoch are dominated by dark matter.
Dark matter plays a key role in structure formation because it feels only the force of gravity: the gravitational
Jeans instabilityThe Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter. For stability, the cloud must be in hydrostatic equilibrium,,where is...
which allows compact structures to form is not opposed by any force, such as
radiation pressureRadiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...
. As a result, dark matter begins to collapse into a complex network of
dark matter haloThe dark matter halo is the hypothetical gravitational core of a galaxy, consisting of dark matter.-Rotation curves as evidence of a dark matter halo:...
s well before ordinary matter, which is impeded by pressure forces. Without dark matter, the epoch of galaxy formation would occur substantially later in the universe than is observed.
The physics of structure formation in this epoch is particularly simple, as dark matter perturbations with different
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s evolve independently. As the Hubble radius grows in the expanding universe, it encompasses larger and larger perturbations. During matter domination, all causal dark matter perturbations grow through gravitational clustering. However, the shorter-wavelength perturbations that are encompassed during radiation domination have their growth retarded until matter domination. At this stage, luminous, baryonic matter is expected to simply mirror the evolution of the dark matter, and their distributions should closely trace one another.
It is a simple matter to calculate this "linear power spectrum" and, as a tool for cosmology, it is of comparable importance to the cosmic microwave background. The power spectrum has been measured by galaxy surveys, such as the
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. The project was named after the Alfred P...
, and by surveys of the
Lyman-α forestIn astronomical spectroscopy, the Lyman alpha forest is the sum of absorption lines arising from the Lyman alpha transition of the neutral hydrogen in the spectra of distant galaxies and quasars....
. Since these surveys observe radiation emitted from galaxies and quasars, they do not directly measure the dark matter, but the large scale distribution of galaxies (and of absorption lines in the Lyman-α forest) is expected to closely mirror the distribution of dark matter. This depends on the fact that galaxies will be larger and more numerous in denser parts of the universe, whereas they will be comparatively scarce in rarefied regions.
Nonlinear structure
When the perturbations have grown sufficiently, a small region might become substantially denser than the mean density of the universe. At this point, the physics involved becomes substantially more complicated. When the deviations from homogeneity are small, the dark matter may be treated as a pressureless fluid and evolves by very simple equations. In regions which are significantly denser than the background, the full Newtonian theory of gravity must be included. (The Newtonian theory is appropriate because the masses involved are much less than those required to form a
black holeIn general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, not even light, can escape. The black hole has a one-way surface, called an event horizon, into which objects can fall, but out of which nothing can come...
, and the
speed of gravityIn the context of classical theories of gravitation, the speed of gravity refers to the speed at which a gravitational field propagates. This is the speed at which changes in the distribution of energy and momentum result in noticeable changes in the gravitational field which they produce.The...
may be ignored as the light-crossing time for the structure is still smaller than the characteristic dynamical time.) One sign that the linear and fluid approximations become invalid are that dark matter starts to form
causticsIn optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. Caustic can also refer to the curve to which light rays are tangent, defining a boundary of an envelope of...
in which the trajectories of adjacent particles cross, or particles start to form orbits. These dynamics are generally best understood using
N-body simulationsAn N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity . In cosmology, they are used in cosmology to study processes of non-linear structure formation such as the process of forming galaxy filaments and galaxy halos...
(although a variety of semi-analytic schemes, such as the
Press-Schechter formalismPress-Schechter formalism was described in a famous paper by Press & Schecter ....
, can be used in some cases). While in principle these simulations are quite simple, in practice they are very difficult to implement, as they require simulating millions or even billions of particles. Moreover, despite the large number of particles, each particle typically weighs 10
9 solar massThe solar mass , , is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms or about 332,950 times the mass of the Earth or 1,048 times the mass of Jupiter.The solar mass can be...
es and
discretizationIn mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers...
effects may become significant. The largest such simulation is the recent
Millennium simulationThe Millennium Run, also called the Millennium Simulation because of its size, is the name of a computer N-body simulation which was run in order to investigate how matter in the Universe evolved over time...
.
The result of
N-body simulations suggest that the universe is composed largely of
voidIn astronomy, voids are the empty spaces between filaments, the largest-scale structures in the Universe, that contain very few, or no, galaxies....
s, whose densities might be as low as one tenth the cosmological mean. The matter condenses in large
filamentIn physical cosmology, filaments are the largest known structures in the universe, thread-like structures with a typical length of 50 to 80 h-1 megaparsecs that form the boundaries between large voids in the universe...
s and haloes which have an intricate web-like structure. These form
galaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The name is from the Greek root galaxias [γαλαξίας], meaning "milky," a reference...
groups, clustersGalaxy groups and clusters are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation. They form the densest part of the large scale structure of the universe...
and
superclusterSuperclusters are large groups of smaller galaxy groups and clusters and are among the largest structures of the cosmos.-Existence:The existence of superclusters indicates that the galaxies in our Universe are not uniformly distributed; most of them are drawn together in groups and clusters, with...
s. While the simulations appear to agree broadly with observations, their interpretation is complicated by the understanding of how dense accumulations of dark matter spur galaxy formation. In particular, many more small haloes form than we see in astronomical observations as
dwarf galaxiesA dwarf galaxy is a small galaxy composed of up to several billion stars, a small number compared to our own Milky Way's 200-400 billion stars. The Large Magellanic Cloud, containing over 30 billion stars, is sometimes classified as a dwarf galaxy while others consider it a full-fledged galaxy...
and
globular clusterA globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is...
s. This is known as the galaxy bias problem, and a variety of explanations have been proposed. Most account for it as an effect in the complicated physics of galaxy formation, but some have suggested that it is a problem with our model of
dark matterIn astronomy and cosmology, dark matter is hypothetical matter that is undetectable by its emitted radiation, but whose presence can be inferred from gravitational effects on visible matter...
and that some effect, such as
warm dark matterWarm dark matter has properties intermediate between those of hot dark matter and cold dark matter, causing structure formation to occur bottom-up from above their free-streaming scale, and top-down below their free streaming scale...
, prevents the formation of the smallest haloes.
Gastrophysical evolution
The final stage in evolution comes when baryons condense in the centers of galaxy haloes to form galaxies, stars and
quasarA quasi-stellar radio source is a powerfully energetic and distant galaxy with an active galactic nucleus. Quasars were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than extended...
s. A paradoxical aspect of structure formation is that while dark matter greatly accelerates the formation of dense haloes, because dark matter does not have radiation pressure, the formation of smaller structures from dark matter is impossible because dark matter cannot dissipate angular momentum, whereas ordinary baryonic matter can collapse to form dense objects by dissipating angular momentum through
radiative coolingRadiative cooling is the process by which a body loses heat by radiation. In the case of the earth-atmosphere system it refers to the process by which long-wave radiation is emitted to balance the absorption of short-wave energy from the sun.The exact process by which the earth loses heat is...
. Understanding these processes is an enormously difficult computational problem, because they can involve the physics of gravity,
magnetohydrodynamicsMagnetohydrodynamics is the academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, and hydro- meaning liquid, and...
,
atomic physicsAtomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...
, nuclear reactions,
turbulenceIn fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Flow that is not turbulent is called laminar flow...
and even
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. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
. In most cases, it is not yet possible to perform simulations that can be compared quantitatively with observations, and the best that can be achieved are approximate simulations that illustrate the main qualitative features of a process such as star formation.
Cosmological perturbations
Much of the difficulty, and many of the disputes, in understanding the large-scale structure of the universe can be resolved by understanding the choice of
gaugeGauge 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...
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. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
better. By the
scalar-vector-tensor decompositionIn cosmological perturbation theory, the scalar-vector-tensor decomposition is a decomposition of the most general linearized perturbations of the Friedmann-Robertson-Walker metric into components according to their transformations under spatial rotations. It was first discovered by E. M. Lifshitz...
, the metric includes four
scalarIn 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...
perturbations, two
vectorIn mathematics a vector field is a construction in vector calculus which associates a vector to every point in a subset of Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of...
perturbations, and one
tensorIn mathematics, physics and engineering, a tensor field assigns a tensor to each point of a mathematical space . Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical...
perturbation. Only the scalar perturbations are significant: the vectors are exponentially suppressed in the early universe, and the tensor mode makes only a small (but important) contribution in the form of primordial gravitational radiation and the B-modes of the cosmic microwave background polarization. Two of the four scalar modes may be removed by a physically meaningless coordinate transformation. Which modes are eliminated determine the infinite number of possible
gauge fixingIn the physics of gauge theories, gauge fixing denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field...
s. The most popular gauge is
Newtonian gaugeIn general relativity, Newtonian gauge is a perturbed form of the Friedmann-Robertson-Walker line element. The gauge freedom of general relativity is used to eliminate two scalar degrees of freedom of the metric, so that it can be written as...
(and the closely related conformal Newtonian gauge), in which the retained scalars are the Newtonian potentials Φ and Ψ, which correspond exactly to the Newtonian potential energy from Newtonian gravity. Many other gauges are used, including
synchronous gaugeIn general relativity, a synchronous reference system is a coordinate system in which the metric takes the form,where the Latin indices a and b are summed over the spatial directions and is a spatial metric. Any metric can locally be put into this form by a coordinate transformation...
, which can be an efficient gauge for numerical computation (it is used by
CMBFASTIn physical cosmology, CMBFAST is a computer code, written by Uros Seljak and Matias Zaldarriaga, for computing the anisotropy of the cosmic microwave background. It was the first efficient program to do so, reducing the time taken to compute the anisotropy from several days to a few minutes by...
). Each gauge still includes some unphysical degrees of freedom. There is a so-called gauge-invariant formalism, in which only gauge invariant combinations of variables are considered.
Inflation and initial conditions
The initial conditions for the universe are thought to arise from the scale invariant quantum mechanical fluctuations of
cosmic inflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10
−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density...
. The perturbation of the background energy density at a given point in space is then given by an
isotropicIsotropy is uniformity in all directions. Precise definitions depend on the subject area. The word is made up from Greek iso and tropos . Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary...
,
homogeneousIn mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A special case of this is when the topological group,...
Gaussian random fieldA Gaussian random field is a random field involving Gaussian probability density functions of the variables. The initial conditions of physical cosmology generated by quantum mechanical fluctuations during cosmic inflation are thought to be a Gaussian random field with a nearly scale invariant...
of
meanIn statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
zero. This means that the spatial Fourier transform of – has the following
correlation functionA correlation function is the correlation between random variables at two different points in space or time, usually as a function of the spatial or temporal distance between the points...
s,
where is the three dimensional
Dirac delta functionThe Dirac delta or Dirac's delta is a mathematical construct introduced by theoretical physicist Paul Dirac. Informally, it is a generalized function representing an infinitely sharp peak bounding unit area: a 'function' δ that has the value zero everywhere except at x = 0 where its value is...
and is the length of . Moreover, the spectrum predicted by inflation is nearly scale invariant, which means,
where is a small number. Finally, the initial conditions are adiabatic or isentropic, which means that the fractional perturbation in the entropy of each species of particle is equal.