Static universe

<h2 id="the-einstein-universe">The Einstein universe</h2>
Main article: <a href="/facts/Einstein%2527s_static_universe/GAplBBas">Einstein's static universe</a>
During 1917, Albert Einstein added a positive <a href="/facts/Cosmological_constant/bjMksSA2">cosmological constant</a> to his <a href="/facts/Einstein_equation/j2rJTzW9">equations</a> of <a href="/facts/General_relativity/jVsoIg8X">general relativity</a> to counteract the attractive effects of <a href="/facts/Gravity/bqAN7DdQ">gravity</a> on ordinary matter, which would otherwise cause a static, spatially finite universe to either <a href="/facts/Big_Crunch/bCewhu87">collapse</a> or <a href="/facts/Future_of_an_expanding_universe/ySer1Ltq">expand forever</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a><a class="footnote-ref" id="fnref:3" href="#fn:3">3</a><a class="footnote-ref" id="fnref:4" href="#fn:4">4</a>
This model of the universe became known as the Einstein World or <a href="/facts/Einstein%2527s_static_universe/GAplBBas">Einstein's static universe</a>.
This motivation ended after the proposal by the astrophysicist and Roman Catholic priest <a href="/facts/Georges_Lema%25C3%25AEtre/odTWjQY1">Georges Lemaître</a> that the universe seems to be not static, but expanding. <a href="/facts/Edwin_Hubble/fpX3JlbJ">Edwin Hubble</a> had researched data from the observations made by astronomer <a href="/facts/Vesto_Slipher/ewBeHwIC">Vesto Slipher</a> to confirm a relationship between <a href="/facts/Hubble%2527s_law/FJYfELCP">redshift and distance</a>, which forms the basis for the modern <a href="/facts/Metric_expansion_of_space/f6Uvt79B">expansion paradigm</a> that was introduced by Lemaître. According to <a href="/facts/George_Gamow/n79Pqk8R">George Gamow</a> this caused Einstein to declare this cosmological model, and especially the introduction of the cosmological constant, his "biggest blunder".<a href="https://en.wikipedia.org/wiki/Static_universe#endnote_greatestblunder">[1]</a>
Einstein's static universe is <a href="/facts/Closed_universe/EJFEm9bw">closed</a> (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive <a href="/facts/Cosmological_constant/bjMksSA2">cosmological constant</a> 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 <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a>. The <a href="/facts/Radius_of_curvature_(mathematics)/FYeD7eyl">radius of curvature</a> 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 <a href="/facts/Friedmann%25E2%2580%2593Lema%25C3%25AEtre%25E2%2580%2593Robertson%25E2%2580%2593Walker_metric/b6cdgxyF">Friedmann's solutions</a> 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.
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 <a href="/facts/Matter_density/92p6hh9I">matter density</a>, or the <a href="/facts/Spatial_curvature/jVsoIg8X">spatial curvature</a> 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,<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> most physicists of the twentieth century assumed that the cosmological constant is zero. If so (absent some other form of <a href="/facts/Dark_energy/6bWIYewA">dark energy</a>), the expansion of the universe would be decelerating. However, after <a href="/facts/Saul_Perlmutter/r7pVlRCA">Saul Perlmutter</a>, <a href="/facts/Brian_P._Schmidt/2KBGCHT7">Brian P. Schmidt</a>, and <a href="/facts/Adam_G._Riess/od3WGg9F">Adam G. Riess</a> introduced the theory of an <a href="/facts/Accelerating_universe/F7X1PAMq">accelerating universe</a> during 1998, a positive cosmological constant has been revived as a simple explanation for <a href="/facts/Dark_energy/6bWIYewA">dark energy</a>.
In 1976 <a href="/facts/Irving_Segal/SasFUqI8">Irving Segal</a> revived the static universe in his <a href="/facts/Chronometric_cosmology/SasFUqI8">chronometric cosmology</a>. 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.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a>

<h2 id="requirements-of-a-static-infinite-model">Requirements of a static infinite model</h2>
In order for a static infinite universe model to be viable, it must explain three things:
First, it must explain the intergalactic <a href="/facts/Redshift/Qfl4VjDF">redshift</a>. Second, it must explain the <a href="/facts/Cosmic_microwave_background_radiation/ThB2HkLS">cosmic microwave background radiation</a>. Third, it must have a mechanism to re-create matter (particularly <a href="/facts/Hydrogen/BoYHjl0J">hydrogen</a> 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 <a href="/facts/Stellar_nucleosynthesis/qEQJdJe6">stellar processes</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a><a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> With the absence of such a mechanism, the universe would consist of dead objects such as <a href="/facts/Black_hole/1r2lmkcF">black holes</a> and <a href="/facts/Black_dwarf/oaMHrFSb">black dwarfs</a>.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Milne_model/o9TI8oHe">Milne model</a></li>
<li><a href="/facts/Steady_State_theory/qzDPzmqI">Steady State theory</a></li>
<li><a href="/facts/Plasma_cosmology/ERwIBkVJ">Plasma cosmology</a></li></ul>

<ol><li>^ 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."</li></ol>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Pogge, Richard W. (February 24, 2014). "Essay: The Folly of Giordano Bruno". 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. <a href="http://www.astronomy.ohio-state.edu/~pogge/Essays/Bruno.html" target="_blank">http://www.astronomy.ohio-state.edu/~pogge/Essays/Bruno.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie". Sitzungs. König. Preuss. Akad.: Sitzungsb. König. Preuss. Akad. 142–152. <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). The Principle of Relativity. New York: Metheun & Co. pp. 175–188. <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn: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:1701.07261. Bibcode:2017EPJH...42..431O. doi:10.1140/epjh/e2017-80002-5. S2CID 119461771. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn: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:1311.2763. Bibcode:2014EPJH...39...37N. doi:10.1140/epjh/e2013-40037-6. S2CID 122011477. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Irving Segal (1976): Mathematical cosmology and extragalactic astronomy. Pure and Applied Mathematics Series, Vol. 68. Academic Press. 19 February 1976. ISBN 9780080873848. <a href="9780080873848" target="_blank">9780080873848</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">MacMillan, W.D. 1918. "On stellar evolution". Astrophys. J. 48: 35–49 <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">MacMillan, W.D. 1925. "Some mathematical aspects of cosmology". Science 62: 63–72, 96–99, 121–127. <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
</ol>

Static universe open-in-new

Static universe