# Static universe

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Cosmological model in which the universe does not expand

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In [cosmology](/source/Cosmology), a **static universe** (also referred to as **stationary**, **infinite**, **static infinite** or **static eternal**) is a [cosmological model](/source/Cosmological_model) in which the [universe](/source/Universe) is both [spatially](/source/Space) and [temporally](/source/Time) infinite, and space is neither [expanding](/source/Metric_expansion_of_space) nor contracting. A static infinite universe was first proposed by English astronomer [Thomas Digges](/source/Thomas_Digges) (1546–1595).[1]

In contrast to this model, [Albert Einstein](/source/Albert_Einstein) proposed a temporally infinite but spatially finite model - *static eternal universe* - as his preferred [cosmology](/source/Physical_cosmology) during 1917, in his paper *Cosmological Considerations in the General Theory of Relativity*.

After the discovery of the [redshift-distance relationship](/source/Hubble's_law) (deduced by the inverse correlation of galactic brightness to redshift) by American astronomers [Vesto Slipher](/source/Vesto_Slipher) and [Edwin Hubble](/source/Edwin_Hubble), the Belgian astrophysicist and priest [Georges Lemaître](/source/Georges_Lema%C3%AEtre) interpreted the redshift as evidence of universal expansion and thus a [Big Bang](/source/Big_Bang), whereas Swiss astronomer [Fritz Zwicky](/source/Fritz_Zwicky) proposed that the redshift was caused by the [photons](/source/Photon) losing energy as they passed through the [matter](/source/Matter) and/or [forces](/source/Force_field_(physics)) in intergalactic space. Zwicky's proposal would come to be termed '[tired light](/source/Tired_light)'—a term invented by the major [Big Bang](/source/Big_Bang) proponent [Richard Tolman](/source/Richard_Tolman).

## The Einstein universe

Main article: [Einstein's static universe](/source/Einstein's_static_universe)

During 1917, Albert Einstein added a positive [cosmological constant](/source/Cosmological_constant) to his [equations](/source/Einstein_equation) of [general relativity](/source/General_relativity) to counteract the attractive effects of [gravity](/source/Gravity) on ordinary matter, which would otherwise cause a static, spatially finite universe to either [collapse](/source/Big_Crunch) or [expand forever](/source/Future_of_an_expanding_universe).[2][3][4] This model of the universe became known as the Einstein World or [Einstein's static universe](/source/Einstein's_static_universe).

This motivation ended after the proposal by the astrophysicist and Roman Catholic priest [Georges Lemaître](/source/Georges_Lema%C3%AEtre) that the universe seems to be not static, but expanding. [Edwin Hubble](/source/Edwin_Hubble) had researched data from the observations made by astronomer [Vesto Slipher](/source/Vesto_Slipher) to confirm a relationship between [redshift and distance](/source/Hubble's_law), which forms the basis for the modern [expansion paradigm](/source/Metric_expansion_of_space) that was introduced by Lemaître. According to [George Gamow](/source/George_Gamow) this caused Einstein to declare this cosmological model, and especially the introduction of the cosmological constant, his "biggest blunder".[\[1\]](https://en.wikipedia.org/wiki/Static_universe#endnote_greatestblunder)

Einstein's static universe is [closed](/source/Closed_universe) (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive [cosmological constant](/source/Cosmological_constant) with value precisely Λ E = 4 π G ρ / c 2 {\displaystyle \Lambda _{E}=4\pi G\rho /c^{2}} , where G {\displaystyle G} is Newtonian gravitational constant, ρ {\displaystyle \rho } is the energy density of the matter in the universe and c {\displaystyle c} is the [speed of light](/source/Speed_of_light). The [radius of curvature](/source/Radius_of_curvature_(mathematics)) of space of the Einstein universe is equal to

- R E = Λ E − 1 / 2 = c 4 π G ρ . {\displaystyle R_{E}=\Lambda _{E}^{-1/2}={c \over {\sqrt {4\pi G\rho }}}.}

The Einstein universe is one of [Friedmann's solutions](/source/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric) to Einstein's field equation for dust with density ρ {\displaystyle \rho } , cosmological constant Λ E {\displaystyle \Lambda _{E}} , and radius of curvature R E {\displaystyle R_{E}} . It is the only non-trivial static solution to Friedmann's equations.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*]

Because the Einstein universe soon was recognized to be inherently unstable, it was presently abandoned as a viable model for the universe. It is unstable in the sense that any slight change in either the value of the cosmological constant, the [matter density](/source/Matter_density), or the [spatial curvature](/source/Spatial_curvature) will result in a universe that either expands and accelerates forever or re-collapses to a singularity.

After Einstein renounced his cosmological constant, and embraced the Friedmann-LeMaitre model of an expanding universe,[5] most physicists of the twentieth century assumed that the cosmological constant is zero. If so (absent some other form of [dark energy](/source/Dark_energy)), the expansion of the universe would be decelerating. However, after [Saul Perlmutter](/source/Saul_Perlmutter), [Brian P. Schmidt](/source/Brian_P._Schmidt), and [Adam G. Riess](/source/Adam_G._Riess) introduced the theory of an [accelerating universe](/source/Accelerating_universe) during 1998, a positive cosmological constant has been revived as a simple explanation for [dark energy](/source/Dark_energy).

In 1976 [Irving Segal](/source/Irving_Segal) revived the static universe in his [chronometric cosmology](/source/Chronometric_cosmology). Similar to Zwicky, he ascribed the red shift of distant galaxies to curvature in the cosmos. Though he claimed vindication in astronomic data, others find the results to be inconclusive.[6]

## Requirements of a static infinite model

In order for a static infinite universe model to be viable, it must explain three things:

First, it must explain the intergalactic [redshift](/source/Redshift). Second, it must explain the [cosmic microwave background radiation](/source/Cosmic_microwave_background_radiation). Third, it must have a mechanism to re-create matter (particularly [hydrogen](/source/Hydrogen) atoms) from radiation or other sources in order to avoid a gradual 'running down' of the universe due to the conversion of matter into energy in [stellar processes](/source/Stellar_nucleosynthesis).[7][8] With the absence of such a mechanism, the universe would consist of dead objects such as [black holes](/source/Black_hole) and [black dwarfs](/source/Black_dwarf).

## See also

- [Milne model](/source/Milne_model)

- [Steady State theory](/source/Steady_State_theory)

- [Plasma cosmology](/source/Plasma_cosmology)

## References

1. **[^](#cite_ref-1)** Pogge, Richard W. (February 24, 2014). ["Essay: The Folly of Giordano Bruno"](http://www.astronomy.ohio-state.edu/~pogge/Essays/Bruno.html). *astronomy.ohio-state.edu*. Retrieved 3 April 2016. Bruno is often credited with recognizing that the Copernican system allowed an infinite Universe. In truth, the idea that a heliocentric description of the solar system allowed (or at least did not rule out) an infinite Universe was first proposed by Thomas Digges in 1576 in his *A Perfit Description of the Caelestial Orbes*, in which Digges both presents and extends the Copernican system, suggesting that the Universe was infinite.

1. **[^](#cite_ref-2)** Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie". *Sitzungs. König. Preuss. Akad.*: Sitzungsb. König. Preuss. Akad. 142–152.

1. **[^](#cite_ref-3)** Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). *The Principle of Relativity*. New York: Metheun & Co. pp. 175–188.

1. **[^](#cite_ref-4)** O'Raifeartaigh; et al. (2017). "Einstein's 1917 static model of the universe: a centennial review". *Eur. Phys. J. H*. **42** (3): 431–474. [arXiv](/source/ArXiv_(identifier)):[1701.07261](https://arxiv.org/abs/1701.07261). [Bibcode](/source/Bibcode_(identifier)):[2017EPJH...42..431O](https://ui.adsabs.harvard.edu/abs/2017EPJH...42..431O). [doi](/source/Doi_(identifier)):[10.1140/epjh/e2017-80002-5](https://doi.org/10.1140%2Fepjh%2Fe2017-80002-5). [S2CID](/source/S2CID_(identifier)) [119461771](https://api.semanticscholar.org/CorpusID:119461771).

1. **[^](#cite_ref-5)** Nussbaumer, Harry; O'Keeffe, Michael; Nahm, Werner; Mitton, Simon (2014). "Einstein's conversion from his static to an expanding universe". *European Physical Journal H*. **39** (1): 37–62. [arXiv](/source/ArXiv_(identifier)):[1311.2763](https://arxiv.org/abs/1311.2763). [Bibcode](/source/Bibcode_(identifier)):[2014EPJH...39...37N](https://ui.adsabs.harvard.edu/abs/2014EPJH...39...37N). [doi](/source/Doi_(identifier)):[10.1140/epjh/e2013-40037-6](https://doi.org/10.1140%2Fepjh%2Fe2013-40037-6). [S2CID](/source/S2CID_(identifier)) [122011477](https://api.semanticscholar.org/CorpusID:122011477).

1. **[^](#cite_ref-6)** [Irving Segal](/source/Irving_Segal) (1976): [*Mathematical cosmology and extragalactic astronomy*](https://books.google.com/books?id=zyDYTJ7MmQQC). Pure and Applied Mathematics Series, Vol. 68. [Academic Press](/source/Academic_Press). 19 February 1976. [ISBN](/source/ISBN_(identifier)) [9780080873848](https://en.wikipedia.org/wiki/Special:BookSources/9780080873848).

1. **[^](#cite_ref-7)** MacMillan, W.D. 1918. "On stellar evolution". *Astrophys*. J. 48: 35–49

1. **[^](#cite_ref-8)** MacMillan, W.D. 1925. "Some mathematical aspects of cosmology". *Science* 62: 63–72, 96–99, 121–127.

1. **[^](#ref_greatestblunder)** In George Gamow's autobiography, *My World Line* (1970), he says of Einstein: "Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder of his life."

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Adapted from the Wikipedia article [Static universe](https://en.wikipedia.org/wiki/Static_universe) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Static_universe?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.