The

**age of the universe** is the time elapsed since 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...

posited by the most widely accepted scientific model of

cosmologyCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

. The best current estimate of the age of the universe is 13.75 ± 0.13

billion1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001.In scientific notation, it is written as 109....

years (433.6 x 10

^{15} seconds in SI units, or 13.75 Gigayears) within the

Lambda-CDM concordance modelΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter, which is also known as the cold dark matter model with dark energy...

. It is not known if something existed before the

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...

that appeared at the moment of the Big Bang, nor if time is linear, since the expansion estimated by

Hubble's lawHubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

assumed a linear expansion, and later work indicates there may have been variations. The estimated changes in expansion are calculated to be both positive and negative, so Hubble and later estimates broadly agree.

The uncertainty range of ± 0.13 Ga for the age of the universe has been obtained by the agreement of a number of scientific research projects, such as microwave background radiation

measurementMeasurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

s by

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...

and other probes. Measurements of the cosmic background radiation give the cooling

timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

of the

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...

since the Big Bang, and measurements of the expansion rate of the universe can be used to calculate its approximate age by extrapolating backwards in time.

## Explanation

The

Lambda-CDM concordance modelΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter, which is also known as the cold dark matter model with dark energy...

describes the evolution of the universe from a very uniform, hot, dense primordial state to its present state over a span of about 13.75 billion years of cosmological time. This model is well understood theoretically and strongly supported by recent high-precision astronomical observations such as WMAP. In contrast, theories of the origin of the primordial state remain very speculative. If one extrapolates the Lambda-CDM model backward from the earliest well-understood state, it quickly (within a small fraction of a second) reaches a

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...

called the "Big Bang singularity." This singularity is not considered to have any physical significance, but it is convenient to quote times measured "since the Big Bang" even though they do not correspond to a physically measurable time. For example, "10

^{−6} second after the Big Bang" is a well-defined era in the universe's evolution. In one sense it would be more meaningful to refer to the same era as "13.7 billion years minus 10

^{−6} seconds ago," but this is unworkable since the latter time interval is swamped by uncertainty in the former.

Though the universe might in theory have a longer history, the

International Astronomical UnionThe International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...

presently use "age of the universe" to mean the duration of the Lambda-CDM expansion, or equivalently the elapsed time since the Big Bang in the current observable universe.

## Observational limits

Since the universe must be at least as old as the oldest thing in it, there are a number of observations which put a lower limit on the age of the universe; these include the temperature of the coolest

white dwarfA white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...

s, which gradually cool as they age, and the dimmest

turnoff pointThe turnoff point for a star refers to the point on the Hertzsprung-Russell diagram where it leaves the main sequence after the exhaustion of its main fuel. By plotting the turnoff point of the stars in star clusters, one can estimate the clusters age....

of

main sequenceThe main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...

stars in clusters (lower-mass stars spend a greater amount of time on the main sequence, so the lowest-mass stars that have evolved off of the main sequence set a minimum age). On 23 April 2009 a

gamma-ray burstGRB 090423 is a gamma-ray burst detected by the Swift Gamma-Ray Burst Mission on April 23, 2009 at 07:55:19 UTC. The afterglow of GRB 090423 was detected in the infrared, and allowed astronomers to determine that the redshift of GRB 090423 is z = 8.2, which makes GRB 090423 the second...

was detected which was later confirmed to be over 13 billion years old.

## Cosmological parameters

The problem of determining the age of the universe is closely tied to the problem of determining the values of the cosmological parameters. Today this is largely carried out in the context of the ΛCDM model, where the Universe is assumed to contain normal (baryonic) matter, cold

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...

, radiation (including both

photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s and

neutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

s), and 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...

. The fractional contribution of each to the current energy density of the Universe is given by the density parameters Ω

_{m}, Ω

_{r}, and Ω

_{Λ}. The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with the Hubble parameter

*H*_{0} are the most important.

If one has accurate measurements of these parameters, then the age of the universe can be determined by using the

Friedmann equationThe Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity...

. This equation relates the rate of change in the

scale factorA scale factor is a number which scales, or multiplies, some quantity. In the equation y=Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x...

*a*(

*t*) to the matter content of the Universe. Turning this relation around, we can calculate the change in time per change in scale factor and thus calculate the total age of the universe by

integratingIntegration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

this formula. The age

*t*_{0} is then given by an expression of the form

where

*H*_{0} is the

Hubble parameterHubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

and the function

*F* depends only on the fractional contribution to the universe's energy content that comes from various components. The first observation that one can make from this formula is that it is the Hubble parameter that controls that age of the universe, with a correction arising from the matter and energy content. So a rough estimate of the age of the universe comes from the Hubble time, the inverse of the Hubble parameter, or

.

The Hubble constant

measures how fast the universe is expanding and is usually given in units of kilometers per second per megaparsec (km/s/mpc)—the further away an object is, the faster it recedes. One megaparsec = 3.086×10

^{19} km, so if

*H*_{0} = 71 km/s/mpc,

= 2.30×10

^{−18} s

^{−1}, and the value of Hubble time is 4.35×10

^{17} s or 13.8 billion years.

To get a more accurate number, the correction factor

*F* must be computed. In general this must be done numerically, and the results for a range of cosmological parameter values are shown in the figure. For the WMAP values (Ω

_{m}, Ω

_{Λ}) = (0.266, 0.732), shown by the box in the upper left corner of the figure, this correction factor is nearly one:

*F* = 0.996. For a flat universe without any cosmological constant, shown by the star in the lower right corner,

*F* = is much smaller and thus the universe is younger for a fixed value of the Hubble parameter. To make this figure, Ω

_{r} is held constant (roughly equivalent to holding the CMB temperature constant) and the curvature density parameter is fixed by the value of the other three.

The Wilkinson Microwave Anisotropy Probe (WMAP) was instrumental in establishing an accurate age of the universe, though other measurements must be folded in to gain an accurate number.

CMBCMB can mean:*The IATA airport code for Bandaranaike International Airport, Colombo – Sri Lanka's only international airport*C.M.B., the debut album of American R&B and pop group Color Me Badd...

measurements are very good at constraining the matter content Ω

_{m} and curvature parameter Ω

_{k}. It is not as sensitive to Ω

_{Λ} directly, partly because the cosmological constant only becomes important at low redshift. The most accurate determinations of the Hubble parameter

*H*_{0} come from

Type Ia supernovaA Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

e. Combining these measurements leads to the generally accepted value for the age of the universe quoted above.

The cosmological constant makes the universe "older" for fixed values of the other parameters. This is significant, since before the cosmological constant became generally accepted, the Big Bang model had difficulty explaining why

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 in the Milky Way appeared to be far older than the age of the universe as calculated from the Hubble parameter and a matter-only universe. Introducing the cosmological constant allows the universe to be older than these clusters, as well as explaining other features that the matter-only cosmological model could not.

## WMAP

NASAThe National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

's

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) project's seven-year data release in 2010 estimated the age of the universe to be years (13.75 billion years old, with an uncertainty of plus or minus 110 million years).

However, this age is based on the assumption that the project's underlying model is correct; other methods of estimating the age of the universe could give different ages. Assuming an extra background of relativistic particles, for example, can enlarge the error bars of the WMAP constraint by one order of magnitude.

This measurement is made by using the location of the first acoustic peak in the

microwave backgroundIn cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

power spectrum to determine the size of the decoupling surface (size of universe at the time of recombination). The light travel time to this surface (depending on the geometry used) yields a reliable age for the universe. Assuming the validity of the models used to determine this age, the residual accuracy yields a margin of error near one percent.

## Assumption of strong priors

Calculating the age of the universe is only accurate if the assumptions built into the models being used to estimate it are also accurate. This is referred to as strong priors and essentially involves stripping the potential errors in other parts of the model to render the accuracy of actual observational data directly into the concluded result. Although this is not a valid procedure in all contexts (as noted in the accompanying caveat: "based on the fact we have assumed the underlying model we used is correct"), the age given is thus accurate to the specified error (since this error represents the error in the instrument used to gather the raw data input into the model).

The age of the universe based on the "best fit" to WMAP data "only" is 13.75±0.13 Ga (the other estimate of 13.75±0.11 uses Gaussian

priorIn Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p is the probability distribution that would express one's uncertainty about p before the "data"...

s based on earlier estimates from other studies). This number represents the first accurate "direct" measurement of the age of the universe (other methods typically involve

Hubble's lawHubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

and age of the oldest stars in globular clusters, etc.). It is possible to use different methods for determining the same parameter (in this case – the age of the universe) and arrive at different answers with no overlap in the "errors". To best avoid the problem, it is common to show two sets of uncertainties; one related to the actual measurement and the other related to the systematic errors of the model being used.

An important component to the analysis of data used to determine the age of the universe (e.g. from WMAP) therefore is to use a

Bayesian StatisticalBayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...

analysis, which normalizes the results based upon the priors (i.e. the model). This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.

## History

In the 18th century, the concept that the

age of the EarthThe age of the Earth is 4.54 billion years This age is based on evidence from radiometric age dating of meteorite material and is consistent with the ages of the oldest-known terrestrial and lunar samples...

was millions, if not billions, of years old began to be realized. However, most scientists throughout the 19th century and into the first decades of the 20th century presumed that everything else in the Universe was

Steady StateIn cosmology, the Steady State theory is a model developed in 1948 by Fred Hoyle, Thomas Gold, Hermann Bondi and others as an alternative to the Big Bang theory...

and eternal, with maybe stars coming and going but no changes occurring at the largest scale known at the time.

The first scientific theories indicating that the age of the Universe might be finite were the studies of

thermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, formalized in the mid 19th century. The concept 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...

dictates that if the Universe (or any other closed system) were infinitely old then everything inside would be at the same temperature, and thus there would be no stars and no life. No scientific explanation for this contradiction was put forth at the time. In 1915

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...

published the theory 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...

. Based on Einstein's theory,

Mon. 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...

showed that the Universe cannot be static and must be either expanding or contracting. Einstein himself did not believe this result and so he added what he called 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...

to his equations in an unsuccessful attempt to produce a theory consistent with a Steady State Universe.

The first direct observational evidence that the Universe has a finite age came from the observations of astronomer

Edwin HubbleEdwin Powell Hubble was an American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way - our own galaxy...

published in 1929. Earlier in the 20th century, Hubble and others resolved individual stars within certain

nebulaA nebula is an interstellar cloud of dust, hydrogen gas, helium gas and other ionized gases...

thus determining that they were

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 word galaxy is derived from the Greek galaxias , literally "milky", a...

, similar to, but external to, our Milky Way Galaxy. In addition, these galaxies were very large and very far away.

SpectraThe electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

taken of these distant galaxies showed a

red shift-Science:* Redshift, the increase of wavelength of detected electromagnetic radiation with respect to the original wavelength of the emission* Red shift, an informal term for a bathochromic shift...

in their spectral lines presumably caused by the

Doppler effectThe Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

, thus indicating that these galaxies were speeding away from the Earth. In addition, the further away these galaxies seemed to be, the greater the redshift and thus the faster they seemed to be speeding away. This was the first direct evidence that the Universe is not static but expanding. The first estimate of the age of the Universe came from the calculation of when all of the objects must have started speeding out from the same point. Hubble's initial value for age was very low as the galaxies were assumed to be much closer than later observations found them to be.

The first reasonably accurate measurement of the rate of expansion of the Universe, a numerical value now known as the Hubble constant, was made in 1958 by astronomer

Allan SandageAllan Rex Sandage was an American astronomer. He was Staff Member Emeritus with the Carnegie Observatories in Pasadena, California. He is best known for determining the first reasonably accurate value for the Hubble constant and the age of the universe.-Career:Sandage was one of the most...

. His measured value for the Hubble constant yielded the first good estimate of the age of the Universe, coming very close to the value range generally accepted today.

However Sandage, like Einstein, did not believe his own results at the time of discovery. His value for the age of the Universe was too short to reconcile with the 25 billion year age estimated at that time for the oldest known

starA star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s. Sandage and other astronomers repeated these measurements numerous times, attempting to reduce the Hubble constant and thus increase the resulting age for the Universe. Sandage even proposed new theories of

cosmogonyCosmogony, or cosmogeny, is any scientific theory concerning the coming into existence or origin of the universe, or about how reality came to be. The word comes from the Greek κοσμογονία , from κόσμος "cosmos, the world", and the root of γίνομαι / γέγονα "to be born, come about"...

to explain this discrepancy. This issue was finally resolved by improvements in the theoretical models used for estimating the ages of stars. Presently, using these new models for stellar evolution, the estimated age of the oldest known star is about 13.2 billion years.

The discovery of

microwaveMicrowaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

cosmic background radiation announced in 1965 finally brought an effective end to the remaining scientific uncertainty over the expanding Universe. The space probe

WMAPThe 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...

, launched in 2001, produced data that determines the Hubble constant and the age of the Universe independent of galaxy distances, removing the largest source of error.

## See also

- Age crisis
The Age Crisis is a former problem in physics which incorrectly posited that certain stars must actually be older than the universe itself.For a short time in the mid-1990s, the estimated age of the universe was around 10 billion years...

- Age of the Earth
The age of the Earth is 4.54 billion years This age is based on evidence from radiometric age dating of meteorite material and is consistent with the ages of the oldest-known terrestrial and lunar samples...

- Metric expansion of space
The 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...

- Red shift observations in astronomy
- Observable universe
In 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...

- Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...

- Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

- Hubble Deep Field
The Hubble Deep Field is an image of a small region in the constellation Ursa Major, constructed from a series of observations by the Hubble Space Telescope. It covers an area 2.5 arcminutes across, two parts in a million of the whole sky, which is equivalent in angular size to a 65 mm tennis...

- Multiverse
The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...

## External links