Age of the universe

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In physical cosmology, the age of the universe is the time elapsed since the Big Bang. The current measurement of the age of the universe is around 13.8 billion years (as of 2015 [1] ) – 13.787±0.020 billion years within the Lambda-CDM concordance model (as of 2018 [2] ). The uncertainty 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 by the Planck spacecraft, the Wilkinson Microwave Anisotropy Probe and other space probes. Measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang, [3] and measurements of the expansion rate of the universe can be used to calculate its approximate age by extrapolating backwards in time.



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 13.8 billion years [4] 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 singularity. This is known as the "initial singularity" or the "Big Bang 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 "13.8 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 [5] 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 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 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).

Cosmological parameters

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 (O). 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 closed universe has the least age. Mplwp universe scale evolution.svg
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 closed universe has the least age.
The value of the age correction factor, F, is shown as a function of two cosmological parameters: the current fractional matter density Om and cosmological constant density OL. 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. Age Universe Planck 2013.png
The value of the age correction factor, F, is shown as a function of two cosmological parameters: the current fractional matter density Ωm and cosmological constant density ΩΛ. 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. 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 Ωm, Ωr, 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 parameter , 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 equation. This equation relates the rate of change in the 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 integrating this formula. The age t0 is then given by an expression of the form

where is the 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 around 69 km/s/Mpc, the Hubble time evaluates to = 14.5 billion years. [6]

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 Planck valuesm, ΩΛ) = (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 = 23 is much smaller and thus the universe is younger for a fixed value of the Hubble parameter. To make this figure, Ωr 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.

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 Ωm [7] and curvature parameter Ωk. [8] It is not as sensitive to ΩΛ directly, [8] partly because the cosmological constant becomes important only at low redshift. The most accurate determinations of the Hubble parameter H0 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. [9] [10] 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. [11]


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). [3]

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. [12]

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 percent. [13]


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. By combining the Planck data with external data, the best combined estimate of the age of the universe is (13.799±0.021)×109 years old. [1] [14]

In the table below, figures are within 68% confidence limits for the base ΛCDM model.


Cosmological parameters from 2015 Planck results [1]
Age of the universe
Hubble constant

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"[ citation needed ]), 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 2015 data alone is 13.813±0.038 billion years (the estimate of 13.799±0.021 billion years uses Gaussian priors based on earlier estimates from other studies to determine the combined uncertainty). 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) therefore is to use a Bayesian statistical analysis, which normalizes the results based upon the priors (i.e. the model). [13] This quantifies any uncertainty in the accuracy of a measurement due to a particular model used. [15] [16]



In the 18th century, the concept that the age of the Earth was millions, if not billions, of years began to appear. However, 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, 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 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 [17] 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 Slipher, combined with distances to the 'nebulae' (galaxies) by Edwin Hubble in a work published in 1929. [18] 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, our 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 to us) 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 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 Sandage. [19] His measured value for the Hubble constant came 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[ further explanation needed ] was too short to reconcile with the 25-billion-year age estimated at that time for the oldest known stars. 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 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 2013, using the latest models for stellar evolution, the estimated age of the oldest known star is 14.46±0.8 billion years. [20]

The discovery of microwave cosmic background radiation announced in 1965 [21] 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 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 our galaxy, but from outside our own galaxy, 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 which 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 to its current figure.

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. [13]

See also

Related Research Articles

Big Bang Cosmological model

The Big Bang theory is a cosmological model of the observable universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of extremely high density and high temperature, and offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure.

Physical cosmology Branch of astronomy

Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood. Physical cosmology, as it is now understood, began with the development in 1915 of Albert Einstein's general theory of relativity, followed by major observational discoveries in the 1920s: first, Edwin Hubble discovered that the universe contains a huge number of external galaxies beyond the Milky Way; then, work by Vesto Slipher and others showed that the universe is expanding. These advances made it possible to speculate about the origin of the universe, and allowed the establishment of the Big Bang theory, by Georges Lemaître, as the leading cosmological model. A few researchers still advocate a handful of alternative cosmologies; however, most cosmologists agree that the Big Bang theory best explains the observations.

Cosmic microwave background Electromagnetic radiation as a remnant from an early stage of the universe in Big Bang cosmology

The cosmic microwave background, in Big Bang cosmology, is electromagnetic radiation as a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space. It is an important source of data on the early universe because it is the oldest electromagnetic radiation in the universe, dating to the epoch of recombination. With a traditional optical telescope, the space between stars and galaxies is completely dark. However, a sufficiently sensitive radio telescope shows a faint background noise, or glow, almost isotropic, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1965 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s, and earned the discoverers the 1978 Nobel Prize in Physics.

Universe All of space and time and their contents

The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. While the spatial size of the entire universe is unknown, it is possible to measure the size of the observable universe, which is currently estimated to be 93 billion light-years in diameter. In various multiverse hypotheses, a universe is one of many causally disconnected constituent parts of a larger multiverse, which itself comprises all of space and time and its contents; as a consequence, ‘the universe’ and ‘the multiverse’ are synonymous in such theories.

Accelerating expansion of the universe rate of increase in the expansion of the universe

The accelerating expansion of the universe is the observation that the expansion of the universe is such that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.

Hubbles law Observation in physical cosmology

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from the Earth at velocities proportional to their distance. In other words, the further they are the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit to the red end of the spectrum.

Shape of the universe The local and global geometry of the universe

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Wilkinson Microwave Anisotropy Probe space observatory

The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP), was a spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic microwave background (CMB) – the radiant heat remaining from the Big Bang. Headed by Professor Charles L. Bennett of Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University. The WMAP spacecraft was launched on June 30, 2001 from Florida. The WMAP mission succeeded the COBE space mission and was the second medium-class (MIDEX) spacecraft in the NASA Explorers program. In 2003, MAP was renamed WMAP in honor of cosmologist David Todd Wilkinson (1935–2002), who had been a member of the mission's science team. After nine years of operations, WMAP was switched off in 2010, following the launch of the more advanced Planck spacecraft by European Space Agency in 2009.

Ultimate fate of the universe Range of cosmological hypotheses and scenarios describing the eventual fate of the universe as we know it

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Big Rip cosmological model based on an exponentially increasing rate of expansion

In physical cosmology, the Big Rip is a hypothetical cosmological model concerning the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, and even spacetime itself, is progressively torn apart by the expansion of the universe at a certain time in the future. According to the standard model of cosmology the scale factor of the universe is known to be accelerating and, in the future era of cosmological constant dominance, will increase exponentially. However, this expansion is similar for every moment of time, and is characterized by an unchanging, small Hubble constant, effectively ignored by any bound material structures. By contrast in the Big Rip scenario the Hubble constant increases to infinity in a finite time.

Observable universe all matter that can be observed from the Earth at the present time

The observable universe is a spherical region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. There are at least 2 trillion galaxies in the observable universe. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe has a spherical volume centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.

Observational cosmology cosmology

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Allan Sandage astrophysicist

Allan Rex Sandage was an American astronomer. He was Staff Member Emeritus with the Carnegie Observatories in Pasadena, California. He determined the first reasonably accurate values for the Hubble constant and the age of the universe.

The relative expansion of the universe is parametrized by a dimensionless scale factor. Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations.

Lambda-CDM model Model of big-bang cosmology

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Structure formation Formation of galaxies, galaxy clusters and larger structures from small early density fluctuations

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Dark flow A possible non-random component of the peculiar velocity of galaxy clusters

In astrophysics, dark flow is a theoretical non-random component of the peculiar velocity of galaxy clusters. The actual measured velocity is the sum of the velocity predicted by Hubble's Law plus a possible small and unexplained velocity flowing in a common direction.

Dark energy unknown property in cosmology that causes the expansion of the universe to accelerate.

In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from supernovae measurements, which showed that the universe does not expand at a constant rate; rather, the expansion of the universe is accelerating. Understanding the evolution of the universe requires knowledge of its starting conditions and its composition. Prior to these observations, the only forms of matter-energy known to exist were ordinary matter, dark matter, and radiation. Measurements of the cosmic microwave background suggest the universe began in a hot Big Bang, from which general relativity explains its evolution and the subsequent large scale motion. Without introducing a new form of energy, there was no way to explain how an accelerating universe could be measured. Since the 1990s, dark energy has been the most accepted premise to account for the accelerated expansion. As of 2020, there are active areas of cosmology research aimed at understanding the fundamental nature of dark energy: is it a feature of measurement errors, or do modifications to general relativity need to be made?

The cosmic age problem is a historical problem in astronomy concerning the age of the universe. The problem was that at various times in the 20th century, some objects in the universe were estimated to be older than the time elapsed since the Big Bang, as estimated from measurements of the expansion rate of the universe known as the Hubble constant, denoted H0. (This is more correctly called the Hubble parameter, since it generally varies with time). If so, this would represent a contradiction, since objects such as galaxies, stars and planets could not have existed in the extreme temperatures and densities shortly after the Big Bang.


  1. 1 2 3 Planck Collaboration (2016). "Planck 2015 results. XIII. Cosmological parameters (See PDF, page 32, Table 4, Age/Gyr, last column)". Astronomy & Astrophysics. 594: A13. arXiv: 1502.01589 . Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830.
  2. Planck Collaboration (2018). "Planck 2018 results. VI. Cosmological parameters (See PDF, page 15, Table 2, Age/Gyr, last column)". arXiv: 1807.06209 .Cite journal requires |journal= (help)
  3. 1 2 Bennett, C.L.; et al. (2013). "Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results". The Astrophysical Journal Supplement Series. 208 (2): 20. arXiv: 1212.5225 . Bibcode:2013ApJS..208...20B. doi:10.1088/0067-0049/208/2/20.
  4. "Cosmic Detectives". European Space Agency. 2 April 2013. Retrieved 2013-04-15.
  5. Chang, K. (9 March 2008). "Gauging Age of Universe Becomes More Precise". The New York Times .
  6. Liddle, A. R. (2003). An Introduction to Modern Cosmology (2nd ed.). Wiley. p.  57. ISBN   978-0-470-84835-7.
  7. Hu, W. "Animation: Matter Content Sensitivity. The matter-radiation ratio is raised while keeping all other parameters fixed". University of Chicago. Archived from the original on 23 February 2008. Retrieved 2008-02-23.
  8. 1 2 Hu, W. "Animation: Angular diameter distance scaling with curvature and lambda". University of Chicago. Archived from the original on 23 February 2008. Retrieved 2008-02-23.
  9. "Globular Star Clusters". SEDS. 1 July 2011. Archived from the original on 24 February 2008. Retrieved 2013-07-19.
  10. Iskander, E. (11 January 2006). "Independent age estimates". University of British Columbia. Archived from the original on 6 March 2008. Retrieved 2008-02-23.
  11. Ostriker, J. P.; Steinhardt, P. J. (1995). "Cosmic Concordance". arXiv: astro-ph/9505066 .
  12. de Bernardis, F.; Melchiorri, A.; Verde, L.; Jimenez, R. (2008). "The Cosmic Neutrino Background and the Age of the Universe". Journal of Cosmology and Astroparticle Physics . 2008 (3): 20. arXiv: 0707.4170 . Bibcode:2008JCAP...03..020D. doi:10.1088/1475-7516/2008/03/020.
  13. 1 2 3 Spergel, D. N.; et al. (2003). "First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters". The Astrophysical Journal Supplement Series . 148 (1): 175–194. arXiv: astro-ph/0302209 . Bibcode:2003ApJS..148..175S. doi:10.1086/377226.
  14. Lawrence, C. R. (18 March 2015). "Planck 2015 Results" (PDF). Archived from the original (PDF) on 2016-11-24. Retrieved 24 November 2016.
  15. Loredo, T. J. (1992). "The Promise of Bayesian Inference for Astrophysics" (PDF). In Feigelson, E. D.; Babu, G. J. (eds.). Statistical Challenges in Modern Astronomy. Springer-Verlag. pp. 275–297. Bibcode:1992scma.conf..275L. doi:10.1007/978-1-4613-9290-3_31. ISBN   978-1-4613-9292-7.
  16. Colistete, R.; Fabris, J. C.; Concalves, S. V. B. (2005). "Bayesian Statistics and Parameter Constraints on the Generalized Chaplygin Gas Model Using SNe ia Data". International Journal of Modern Physics D . 14 (5): 775–796. arXiv: astro-ph/0409245 . Bibcode:2005IJMPD..14..775C. doi:10.1142/S0218271805006729.
  17. Einstein, A. (1915). "Zur allgemeinen Relativitätstheorie". Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (in German): 778–786. Bibcode:1915SPAW.......778E.
  18. Hubble, E. (1929). "A relation between distance and radial velocity among extra-galactic nebulae". Proceedings of the National Academy of Sciences . 15 (3): 168–173. Bibcode:1929PNAS...15..168H. doi:10.1073/pnas.15.3.168. PMC   522427 . PMID   16577160.
  19. Sandage, A. R. (1958). "Current Problems in the Extragalactic Distance Scale". The Astrophysical Journal . 127 (3): 513–526. Bibcode:1958ApJ...127..513S. doi:10.1086/146483.
  20. Bond, H. E.; Nelan, E. P.; Vandenberg, D. A.; Schaefer, G. H.; Harmer, D. (2013). "HD 140283: A Star in the Solar Neighborhood that Formed Shortly After the Big Bang". The Astrophysical Journal . 765 (12): L12. arXiv: 1302.3180 . Bibcode:2013ApJ...765L..12B. doi:10.1088/2041-8205/765/1/L12.
  21. Penzias, A. A.; Wilson, R .W. (1965). "A Measurement of Excess Antenna Temperature at 4080 Mc/s". The Astrophysical Journal . 142: 419–421. Bibcode:1965ApJ...142..419P. doi:10.1086/148307.