age of the universe

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In
physical cosmology Physical cosmology is a branch of cosmology Cosmology (from Ancient Greek, Greek κόσμος, ''kosmos'' "world" and -λογία, ''-logia'' "study of") is a branch of astronomy concerned with the study of the chronology of the universe. P ...
, the age of the universe is the
time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component qua ...
elapsed since the
Big Bang The Big Bang Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

. Today, astronomers have derived two different measurements of the age of the
universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development ...

: a measurement based on the observations of a distant, infant state of the universe, whose results are an age of around 13.77 billion years (as of 2018),
billion A billion is a number with two distinct definitions: *1,000,000,000 1,000,000,000 (one billion, short scale; one thousand million or milliard, yard, long scale) is the natural number In mathematics, the natural numbers are those used for ...
years within the Lambda-CDM concordance model as of 2018; and a measurement based on the observations of the local, modern universe which suggest a younger universe. The
uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially o ...
of the first kind of measurement has been narrowed down to 20 million years, based on a number of studies which all gave extremely similar figures for the age. These include studies of the
microwave background radiation The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and ratio ...
by the ''Planck'' spacecraft, the
Wilkinson Microwave Anisotropy Probe The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP), is an inactive uncrewed spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic micr ...
and other space probes. Measurements of the cosmic background radiation give the cooling time of the universe 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. The range of the estimate is also within the range of the estimate for the oldest observed star in the universe.

# Explanation

The Lambda-CDM concordance model describes the evolution of the universe from a very uniform, hot, dense primordial state to its present state over a span of about 13.77 billion years of
cosmological time Cosmic time, or cosmological time, is the time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the past, through the ...
. This model is well understood theoretically and strongly supported by recent high-precision
astronomical observation Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical mo ...
s such as
WMAP The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP), is an inactive uncrewed spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic microw ...
. 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
singularity Singularity or singular point may refer to: Science, technology, and mathematics Mathematics * Mathematical singularity, a point at which a given mathematical object is not defined or not "well-behaved", for example infinite or not differentiabl ...
. This is known as the "
initial singularity The initial singularity is a singularity predicted by some models of the Big Bang theory The Big Bang theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The pro ...
" or the "
Big Bang The Big Bang Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

singularity". This singularity is not understood as having a physical significance in the usual sense, 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 seconds after the Big Bang" is a well-defined era in the universe's evolution. If one referred to the same era as "13.77 billion years minus 10−6 seconds ago", the precision of the meaning would be lost because the minuscule latter time interval is eclipsed by uncertainty in the former. Though the universe might in theory have a longer history, the
International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) exists to promote and safeguard the science of astronomy through international cooperation, assign official names and designations to celestial ...
presently uses the term "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 The observable universe is a ball-shaped region of the universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang th ...
.

# Observational limits

Since the universe must be at least as old as the oldest things 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 dwarf A white dwarf, also called a degenerate dwarf, is a stellar core remnant composed mostly of electron-degenerate matter Degenerate matter is a highly dense state of fermionic matter in which the Pauli exclusion principle exerts significant ...

s, which gradually cool as they age, and the dimmest
turnoff point The 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. It is often referred to as the main sequence turnoff. By plotting the turnoff point of the ...
of
main sequence In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar Color index, color versus Absolute magnitude, brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams afte ...
stars A star is an astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. ...

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

# Cosmological parameters

400px, The age of the universe can be determined by measuring the Hubble constant today and extrapolating back in time with the observed value of density parameters (Ω). Before the discovery of dark energy, it was believed that the universe was matter-dominated (Einstein–de Sitter universe, green curve). Note that the de Sitter universe has infinite age, while the Big Crunch, closed universe has the least age. 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 matter, radiation (including both photons and neutrinos), and a cosmological constant. The fractional contribution of each to the current energy density of the universe is given by the density parameters Ω''m'', Ω''r'', and ΩΛ. 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 constant, 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 equations, Friedmann equation. This equation relates the rate of change in the scale factor (cosmology), scale factor ''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 Integral, integrating this formula. The age ''t''0 is then given by an expression of the form :$t_0 = \frac F\left(\Omega_r,\Omega_m,\Omega_\Lambda,\dots\right)$ where $H_0$ is the Hubble's law, Hubble parameter 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. With a value for $H_0$ around , the Hubble time evaluates to $1/H_0$ = 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 Lambda CDM model, Planck values (Ω''m'', Ω''Λ'') = (0.3086, 0.6914), shown by the box in the upper left corner of the figure, this correction factor is about ''F'' = 0.956. 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 Cosmic Microwave Background, CMB temperature constant) and the curvature density parameter is fixed by the value of the other three. Apart from the Planck satellite, 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. CMB measurements are very good at constraining the matter content Ω''m'' and curvature parameter Ω''k''. It is not as sensitive to ΩΛ directly, partly because the cosmological constant becomes important only at low redshift. The most accurate determinations of the Hubble parameter ''H''0 come from Type Ia supernovae. 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 clusters 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

NASA's
Wilkinson Microwave Anisotropy Probe The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP), is an inactive uncrewed spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic micr ...
(WMAP) project's Wilkinson Microwave Anisotropy Probe#Nine-year data release, nine-year data release in 2012 estimated the age of the universe to be years (13.772 billion years, with an uncertainty of plus or minus 59 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 cosmic microwave background radiation, microwave background power spectrum to determine the size of the decoupling surface (size of the 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.

# Planck

In 2015, the Planck (spacecraft), Planck Collaboration estimated the age of the universe to be billion years, slightly higher but within the uncertainties of the earlier number derived from the WMAP data. In the table below, figures are within 68% Confidence interval, confidence limits for the base Lambda-CDM model, ΛCDM model. Legend: *TT, TE, EE: Planck Cosmic microwave background (CMB) Spectral density, power spectra *lowP: Planck Polarization (waves), polarization data in the low-ℓ likelihood *lensing: CMB Gravitational lens, lensing reconstruction *ext: External data (BAO+JLA+H0). BAO: Baryon acoustic oscillations, JLA: Joint Light curve, Light-curve Analysis, H0: Hubble's law, Hubble constant In 2018, the Planck Collaboration updated its estimate for the age of the universe to billion years.

# Assumption of strong priors

Calculating the age of the universe is accurate only 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 Planck (spacecraft)#2018 data release, Planck 2018 data alone is billion years. This number represents an accurate "direct" measurement of the age of the universe (other methods typically involve Hubble's law and the 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 Planck (spacecraft), Planck) therefore is to use a Bayesian statistics, Bayesian statistical 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

Big Bang The Big Bang Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

and could prove whether the Big Bang theory was correct. The two teams realized that the detected noise was in fact radiation left over from the Big Bang, and that this was strong evidence that the theory was correct. Since then, a great deal of other evidence has strengthened and confirmed this conclusion, and refined the estimated age of the universe to its current figure. The space probes WMAP, launched in 2001, and Planck (spacecraft), Planck, launched in 2009, produced data that determines the Hubble constant and the age of the universe independent of galaxy distances, removing the largest source of error.

* Age of the Earth * Anthropic principle * Cosmic Calendar (age of universe scaled to a single year) * Cosmology * Dark Ages Radio Explorer * Expansion of the universe * Hubble Deep Field * Illustris project * Multiverse * Observable universe * Redshift#Observations in astronomy, Redshift observations in astronomy * Static universe * ''The First Three Minutes'' (1977 book by Steven Weinberg) * Timeline of the far future: expected remaining lifetime of the Earth; Solar System; the universe

# References

Ned Wright's Cosmology Tutorial
* *Wayne Hu'

* *SEDS page o

*Douglas Scot

*KryssTa

Space and Time scaled for the beginner.
iCosmos: Cosmology Calculator (With Graph Generation)
(American Institute of Physics) {{DEFAULTSORT:Age Of The Universe Physical cosmology Big Bang Cosmogony