Age of the universe
The universe is ancient, vast, and full of wonders — but how old, exactly, is it? For millennia, this question was the stuff of myth and philosophy, yet modern science has transformed it into a surprisingly precise number. Join us as we journey through the cosmic quest to uncover the birth certificate of everything. Early scientific thought often favored an eternal, static universe, a view that was systematically overturned by observational evidence and theoretical breakthroughs. The age of the universe is primarily determined by two converging methods: studying the cosmic microwave background from the early universe and measuring the expansion rate of distant galaxies today. Modern cosmological models, particularly the Lambda-CDM model, consistently pinpoint the universe's age to an astonishingly precise 13.787 billion years, a testament to scientific collaboration and technological advancement.
AI Summary
The universe is ancient, vast, and full of wonders — but how old, exactly, is it? For millennia, this question was the stuff of myth and philosophy, yet modern science has transformed it into a surprisingly precise number. Join us as we journey through the cosmic quest to uncover the birth certificate of everything.
- Early scientific thought often favored an eternal, static universe, a view that was systematically overturned by observational evidence and theoretical breakthroughs.
- The age of the universe is primarily determined by two converging methods: studying the cosmic microwave background from the early universe and measuring the expansion rate of distant galaxies today.
- Modern cosmological models, particularly the Lambda-CDM model, consistently pinpoint the universe's age to an astonishingly precise 13.787 billion years, a testament to scientific collaboration and technological advancement.
Measuring Cosmic Time
In the realm of physical cosmology, the 'age of the universe' isn't just a number; it's the cosmic time elapsed since the universe's very beginning — the Big Bang. Think of it as winding the universe's expansion backward, like a film in reverse, until all matter was compressed into an incredibly hot, dense state.
Today, our best estimate, supported by a wealth of data, pegs this age at approximately 13.787 billion years. But arriving at this figure was a monumental scientific undertaking, challenging long-held beliefs and pushing the boundaries of human observation and theory.
An Eternal Universe?
For most of history, and even into the early 20th century, many scientists imagined the universe as static and eternal. Stars might come and go, but the grand cosmic stage itself was thought to be unchanging, without a true beginning or end. Earth, by comparison, was already suspected to be millions, if not billions, of years old.
However, a groundbreaking scientific principle — thermodynamics, formalized in the mid-19th century — hinted at a problem. The concept of entropy states that in an infinitely old, closed system like the universe, everything should have reached a uniform temperature. This would mean no stars, no energy flows, and certainly no life. It was a profound contradiction to the vibrant universe we observe.
Einstein's Static Universe
Then came Albert Einstein. In 1915, his theory of General Relativity revolutionized our understanding of gravity and spacetime. Two years later, he applied it to the entire cosmos, creating the first cosmological model. To reconcile his equations with the prevailing idea of a static universe, Einstein famously introduced a 'cosmological constant' into his equations.
This equation, known as the Einstein field equations with a cosmological constant ($\Lambda$), aimed to balance the gravitational pull of matter, preventing the universe from collapsing or expanding. However, it was later shown to be unstable by Arthur Eddington — a mere nudge would cause it to either expand or contract.
R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}Hubble's Revelation
The first truly direct observational evidence against a static universe arrived with Edwin Hubble's work in 1929. Combining Vesto M. Slipher's measurements of 'recession velocities' with his own distance calculations to what were then called 'nebulae' (which Hubble and others had identified as distant galaxies), a revolutionary pattern emerged.
Hubble observed that distant galaxies exhibited a 'redshift' in their light spectra, indicating they were moving away from us. Even more profound, the farther away a galaxy was, the faster it appeared to recede. This stunning correlation, now known as Hubble's Law, was the undeniable proof: the universe was not static; it was expanding!
This equation describes Hubble's Law, where 'v' is the recession velocity of a galaxy, 'D' is its distance, and 'H₀' is the Hubble constant. It essentially says that the universe is stretching, carrying galaxies further apart. Running this expansion backward allowed the first rough estimates of the universe's age, though Hubble's initial calculation was much too low due to underestimating cosmic distances.
v = H_0 D
The Cosmic Echo
While Hubble showed the universe was expanding, the ultimate confirmation of a hot, dense beginning — the Big Bang — came in 1965 with the accidental discovery of the Cosmic Microwave Background (CMB) radiation. Arno Penzias and Robert Wilson, working with a supersensitive radio antenna, detected a persistent, mysterious 'hiss' coming from every direction in the sky.
They initially couldn't explain this low-level microwave noise, trying everything from pigeons to faulty equipment. Unbeknownst to them, a team led by Robert Dicke at Princeton was actively searching for exactly this — the faint afterglow, the 'echo,' of the Big Bang itself. Their combined realization confirmed that the detected noise was indeed radiation left over from the universe's infancy.
The CMB proved to be the smoking gun for the Big Bang model, solidifying the idea of a universe with a finite age. It also provided a crucial 'baby picture' of the universe, allowing scientists to begin measuring its properties with unprecedented accuracy.
The ΛCDM Model: Our Cosmic Blueprint
Today, our understanding of the universe's age is deeply rooted in the Lambda-CDM (ΛCDM) concordance model. This model, often called the 'standard model of cosmology,' describes a universe composed of normal (baryonic) matter, cold dark matter, radiation (photons and neutrinos), and — crucially — a cosmological constant, represented by Lambda (Λ), which accounts for dark energy.
The key to calculating the universe's age within this model lies in precisely measuring several cosmological parameters. These include the Hubble constant (H₀), which describes the current expansion rate, and the density parameters (Ωm, Ωr, ΩΛ), which tell us the fractional contribution of matter, radiation, and dark energy to the universe's total energy density.
The Friedmann Equation
With these parameters in hand, we can use the Friedmann equation. This powerful equation from General Relativity relates the universe's expansion rate to its matter and energy content. By effectively 'integrating' this equation backward in time, from its current state to the Big Bang, we can calculate the total age of the universe (t₀).
This intimidating-looking integral calculates the age (t₀) as a function of the Hubble constant (H₀) and the various density parameters (Ω). Notice that the term 1/H₀, known as the Hubble time, provides a rough estimate — about 14.5 billion years. The integral serves as a 'correction factor' based on the universe's composition.
t_0 = \frac{1}{H_0} \int_{0}^{1} \frac{da}{\sqrt{\Omega_{\rm{m}}a^{-1} + \Omega_{\rm{rad}}a^{-2} + \Omega_{\Lambda}a^{2} + (1-\Omega_{\rm{m}}-\Omega_{\rm{rad}}-\Omega_{\Lambda})}}The Dark Energy Revelation
A crucial realization in calculating the universe's age involved 'dark energy' (represented by the cosmological constant, Λ). Before its widespread acceptance, the calculated age of the universe from a matter-only model was awkwardly younger than some of the oldest observed star clusters, like globular clusters in the Milky Way.
Introducing dark energy into the model changed everything. Its repulsive force effectively slowed down the early expansion and then accelerated the later expansion, meaning the universe has been expanding for longer than a matter-only model would suggest. This elegant solution allowed the universe to be older than its oldest stellar inhabitants, solving a major cosmological puzzle.
Cosmic Precision Instruments
To achieve such high precision, scientists rely on sophisticated space observatories. NASA's Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001, and the European Space Agency's Planck spacecraft, launched in 2009, were instrumental. These missions meticulously mapped the cosmic microwave background, providing exquisite details about the early universe.
By analyzing tiny temperature fluctuations in the CMB, WMAP and Planck could constrain the cosmological parameters with remarkable accuracy, independent of measuring galaxy distances. This removed one of the largest sources of error in previous age estimates. For example, WMAP's 2012 data release estimated the age at 13.772 ± 0.059 billion years.
The Planck Collaboration further refined this, updating the estimate in 2018 to an incredibly precise 13.787 ± 0.020 billion years. This precision is a testament to the power of the ΛCDM model and the consistency of observational data.
Observational Checks
While CMB observations provide an age from the 'baby universe,' other astronomical observations act as crucial cross-checks, setting lower limits on the universe's age. For instance, studying the coolest white dwarfs, which gradually dim and cool over billions of years, helps establish a minimum age.
Similarly, analyzing the 'turnoff point' of stars in ancient globular clusters provides another stellar clock. Lower-mass stars burn their fuel more slowly, staying on the 'main sequence' longer. The point at which the lowest-mass stars begin to evolve off the main sequence in a cluster gives a strong indication of its minimum age — and thus, a minimum age for the universe.
These 'stellar age' estimates, now enhanced by advanced stellar evolution models, align beautifully with the age derived from the CMB, confirming our cosmic timeline. The oldest known stars are estimated to be around 13.8 ± 0.4 billion years old, perfectly consistent with the universe's overall age.
Lookback Time
When we observe distant astronomical objects, we're essentially looking back in time. The light from a galaxy 10 billion light-years away has traveled for 10 billion years, showing us that galaxy as it appeared 10 billion years ago. This concept is called 'lookback time' (tL).
Lookback time (tL) is simply the difference between the current age of the universe (t₀) and the age of the universe at the moment the light was emitted (te). It depends on an object's redshift and, like the universe's age, on the specific cosmological parameters adopted in our models.
t_L(z) = t_0 - t_e(z)
So, from philosophical questions to precise measurements, the journey to pinpoint the age of the universe showcases humanity's relentless curiosity and our growing ability to decode the grand narrative written across the cosmos.
Article
Age of the universe
In Big Bang models of physical cosmology, the age of the universe is the cosmological time back to the point when the scale factor of the universe extrapolates to zero. Using the latest models and the data from the Planck project, the age of the universe is 13.8 billion years. Astronomers have two different approaches to determine the age of the universe. One is based on a particle physics model of the early universe called Lambda-CDM, matched to measurements of features from very early in the history of the universe, like the cosmic microwave background. The other is based on the distance and relative velocity of a series or "ladder" of different kinds of stars, making it depend on local measurements late in the history of the universe. These two methods give slightly different values for the Hubble constant, which is then used in a formula to calculate the age. The range of the estimate is also within the range of the estimate for the oldest observed star in the universe.
History
Age of the universe
<table><thead><tr><th colspan="3">Nature timeline</th></tr></thead><tbody><tr><td colspan="3"></td></tr><tr><td>−13 —–−12 —–−11 —–−10 —–−9 —–−8 —–−7 —–−6 —–−5 —–−4 —–−3 —–−2 —–−1 —–0 —</td><td>Dark AgesReionizationMatter-dominated eraWater on EarthLifeMulticellular lifeVertebrates</td><td></td></tr><tr><td>←</td><td>Earliest stars</td></tr><tr><td>←</td><td>Earliest galaxy</td></tr><tr><td>←</td><td>Earliest quasar / black hole</td></tr><tr><td>←</td><td>Omega Centauri</td></tr><tr><td>←</td><td>Andromeda Galaxy</td></tr><tr><td>←</td><td>Milky Way spirals</td></tr><tr><td>←</td><td>NGC 188 star cluster</td></tr><tr><td>←</td><td>Alpha Centauri</td></tr><tr><td>←</td><td>Accelerated expansion</td></tr><tr><td>←</td><td>Earth / Solar System</td></tr><tr><td>←</td><td>Earliest known life</td></tr><tr><td>←</td><td>Atmospheric oxygen</td></tr><tr><td>←</td><td>Sexual reproduction</td></tr><tr><td>←</td><td>Earliest fungi</td></tr><tr><td>←</td><td>Earliest land plants</td></tr><tr><td>←</td><td>Cambrian explosion</td></tr><tr><td>←</td><td>Earliest mammals</td></tr><tr><td>←</td><td>Earliest apes / humans</td></tr><tr><td colspan="3">(billion years ago)</td></tr></tbody></table>
In the 18th century, the concept that the age of Earth was millions, if not billions, of years began to appear. Nonetheless, most scientists throughout the 19th century and into the first decades of the 20th century presumed that the universe itself was steady state and eternal, possibly with 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 thermodynamics, formalized in the mid-19th century. The concept of entropy 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 Einstein published the theory of general relativity and in 1917 constructed the first cosmological model based on his theory. In order to remain consistent with a steady-state universe, Einstein added what was later called a cosmological constant to his equations. Einstein's model of a static universe was proved unstable by Arthur Eddington.
The first direct observational hint that the universe was not static but expanding came from the observations of 'recession velocities', mostly by Vesto M. Slipher, combined with distances to the 'nebulae' (galaxies) by Edwin Hubble in a work published in 1929. Earlier in the 20th century, Hubble and others resolved individual stars within certain nebulae, thus determining that they were galaxies, similar to, but external to, the Milky Way Galaxy. In addition, these galaxies were very large and very far away. Spectra taken of these distant galaxies showed a red shift in their spectral lines presumably caused by the Doppler effect, thus indicating that these galaxies were moving away from the Earth. In addition, the farther away these galaxies seemed to be (the dimmer they appeared) the greater was their redshift, and thus the faster they seemed to be moving 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 the universe's age was very low, as the galaxies were assumed to be much closer than later observations found them to be.
The lookback time of extragalactic observations by their redshift up to z = 20
The first reasonably accurate measurement of the rate of expansion of the universe, the Hubble constant, was made in 1958 by astronomer Allan Sandage. His measured value for the Hubble constant came very close to the value range generally accepted since then.
Sandage, like Einstein, did not believe his own results at the time of discovery. Sandage proposed new theories of cosmogony to explain this discrepancy. This issue was more or less resolved by improvements in the theoretical models used for estimating the ages of stars. As of 2021, using the latest models for stellar evolution applied to the oldest known stars gives estimated ages of 14.27±0.80 billion years (Methuselah star) and 13.8±4 billion years (BD +17°3248). Both values are compatible with the Planck 2018 number.
The discovery of cosmic microwave background radiation announced in 1965 finally brought an effective end to the remaining scientific uncertainty over the expanding universe. It was a chance result from work by two teams less than 60 miles apart. In 1964, Arno Penzias and Robert Woodrow Wilson were trying to detect radio wave echoes with a supersensitive antenna. The antenna persistently detected a low, steady, mysterious noise in the microwave region that was evenly spread over the sky, and was present day and night. After testing, they became certain that the signal did not come from the Earth, the Sun, or the Milky Way galaxy, but from outside the Milky Way, but could not explain it. At the same time another team, Robert H. Dicke, Jim Peebles, and David Wilkinson, were attempting to detect low level noise that might be left over from the Big Bang 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.
The space probes WMAP, launched in 2001, and 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.
Definition
Age of the universe
Relationship between redshift and age of the universe, from z = [5, 20]
Experimental observations confirm expansion of the universe according to Hubble's law. Since the universe is expanding, the equation for that expansion can be "run backwards" to its starting point. The Lambda-CDM concordance model describes the expansion of the universe from a very uniform, hot, dense primordial state to its existing state over a span of about 13.8 billion years of cosmological time. This model is well understood theoretically and strongly supported by recent high-precision astronomical observations such as WMAP. The International Astronomical Union uses the term "age of the universe" to mean the duration of the Lambda-CDM expansion, or equivalently, the time elapsed within the observable universe since the Big Bang. The expansion rate at any time ${\displaystyle t}$ is called the Hubble parameter ${\displaystyle H(t)\equiv {\frac {\dot {a}}{a}},}$ which is modeled as ${\displaystyle H(a)\equiv {\frac {\dot {a}}{a}}=H{0}{\sqrt {\Omega {\rm {m}}a^{-3}+\Omega {\mathrm {rad} }a^{-4}+\Omega {\Lambda }+(1-\Omega {\rm {m}}-\Omega {\mathrm {rad} }-\Omega {\Lambda })a^{-2}}},}$ where ${\displaystyle \Omega {x}}$ are density parameters, with ${\displaystyle \mathrm {m} }$ for mass (baryons and cold dark matter), ${\displaystyle \mathrm {rad} }$ for radiation (photons plus relativistic neutrinos), and ${\displaystyle \Lambda }$ for dark energy. The value ${\displaystyle H{0}}$, called the Hubble constant, is the Hubble parameter (${\displaystyle t=0}$) and it has units of inverse time. The age of the universe is then defined as ${\displaystyle t{\textrm {age}}={\frac {1}{H{0}}}\int {0}^{1}{\frac {da}{\sqrt {\Omega {\rm {m}}a^{-1}+\Omega {\mathrm {rad} }a^{-2}+\Omega {\Lambda }a^{2}+(1-\Omega {\rm {m}}-\Omega {\mathrm {rad} }-\Omega {\Lambda })}}},}$ The integral is close to 1 so ${\displaystyle H{0}^{-1}}$ is close to the age of the universe.
Observational limits
Age of the universe
Since the universe must be at least as old as the oldest things in it, there are a number of observations that put a lower limit on the age of the universe; these include
• the temperature of the coolest white dwarfs, which gradually cool as they age, and • the dimmest turnoff point of main sequence stars 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).
Before the incorporation of dark energy in the model of cosmic expansion, the age was awkwardly less than the oldest observed astronomical objects. This connection can be used in reverse: the oldest objects found constrain the values of the density parameter for dark energy.
Cosmological parameters
Age of the universe
The age of the universe can be determined by measuring the Hubble constant and extrapolating back in time with the observed value of density parameters (${\displaystyle ~\Omega ~}$). Before the discovery of dark energy, it was believed that the universe was matter-dominated (Einstein–de Sitter universe, green curve). The de Sitter universe has infinite age, while the closed universe has the least age.
The value of the age correction factor, ${\displaystyle ~F~,}$ is shown as a function of two cosmological parameters: the fractional matter density ${\displaystyle ~\Omega {\text{m}}~}$ and cosmological constant density ${\displaystyle ~\Omega {\Lambda }~.}$ The best-fit values of these parameters are shown by the box in the upper left; the matter-dominated universe is shown by the star in the lower right.
The problem of determining the age of the universe is closely tied to the problem of determining the values of the cosmological parameters. 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 energy density of the universe is given by the density parameters${\displaystyle ~\Omega {\text{m}}~,}$ ${\displaystyle ~\Omega {\text{r}}~,}$ and ${\displaystyle ~\Omega {\Lambda }~.}$ 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${\displaystyle ~H{0}~}$, are the most important.
With accurate measurements of these parameters, the age of the universe can be determined by using the Friedmann equation. This equation relates the rate of change in the scale factor${\displaystyle ~a(t)~}$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 integrating this formula. The age${\displaystyle ~t{0}~}$is then given by an expression of the form
${\displaystyle t{0}={\frac {1}{H{0}}}\,F(\,\Omega {\text{r}},\,\Omega {\text{m}},\,\Omega {\Lambda },\,\dots \,)~}$
where${\displaystyle ~H{0}~}$is the Hubble parameter and the function${\displaystyle ~F~}$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 the 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${\displaystyle ~H{0}~}$around 69 km/s/Mpc, the Hubble time evaluates to ${\displaystyle ~1/H{0}=~}$14.5 billion years.
To get a more accurate number, the correction function${\displaystyle ~F~}$must be computed. In general this must be done numerically, and the results for a range of cosmological parameter values are shown in the figure. For the Planck values${\displaystyle ~(\Omega {\text{m}},\Omega {\Lambda })=~}$(0.3086, 0.6914), shown by the box in the upper left corner of the figure, this correction factor is about${\displaystyle ~F=0.956~.}$ For a flat universe without any cosmological constant, shown by the star in the lower right corner,${\displaystyle ~F={2}/{3}~}$is much smaller and thus the universe is younger for a fixed value of the Hubble parameter. To make this figure,${\displaystyle ~\Omega {\text{r}}~}$is held constant (roughly equivalent to holding the cosmic microwave background 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${\displaystyle ~\Omega {\text{m}}~,}$ and curvature parameter ${\displaystyle ~\Omega {\text{k}}~.}$ It is not as sensitive to${\displaystyle ~\Omega {\Lambda }~}$directly, partly because the cosmological constant becomes important only at low redshift. The most accurate determinations of the Hubble parameter${\displaystyle ~H{0}~}$are believed to come from measured brightnesses and redshifts of distant 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.
Lookback time
Age of the universe
Light observed from astronomical objects was emitted when the universe was younger. Astronomers use lookback time, ${\displaystyle t{L}}$, to describe the difference in the age of the universe here and now, ${\displaystyle t{0}}$, from the age at the time of emission, ${\displaystyle t{e}}$: ${\displaystyle t{L}(z)=t{0}-t{e}(z)}$ where t is an age. The lookback time depends on the object's redshift and, like the age of the universe, the cosmological parameters selected.
WMAP
Age of the universe
NASA's Wilkinson Microwave Anisotropy Probe (WMAP) project's nine-year data release in 2012 estimated the age of the universe to be (13.772±0.059)×109 years (13.772 billion years, with an uncertainty of plus or minus 59 million years).
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 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 per cent.
Planck
Age of the universe
In 2015, the Planck Collaboration estimated the age of the universe to be 13.813±0.038 billion years, slightly higher but within the uncertainties of the earlier number derived from the WMAP data. In 2018, the Planck Collaboration updated its estimate for the age of the universe to 13.8 billion years.
Assumption of strong priors
Age of the universe
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. The age given is thus accurate to the specified error, since this 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 2018 data alone is 13.8 billion years. A component to the analysis of data used to determine the age of the universe (e.g. from Planck) is to use a 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.