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A static universe, also referred to as a "stationary" or "infinite" or "static infinite" universe, is a cosmological model in which the Universe is both spatially infinite and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have spatial curvature; that is to say that it is 'flat'. A static infinite universe was first proposed by Giordano Bruno.

In contrast to this model, Albert Einstein proposed a temporally infinite but spatially finite model as his preferred cosmology in 1917, in his paper Cosmological Considerations in the General Theory of Relativity.

After the discovery of the redshift-distance relationship (deduced by the inverse correlation of galactic brightness to redshift) by Vesto Slipher and Edwin Hubble, the Roman Catholic priest Georges LeMaitre interpreted the redshift as proof of universal expansion and thus a Big Bang, whereas Fritz Zwicky proposed that the redshift was caused by the photons losing energy as they passed through the matter and/or forces in intergalactic space. Zwicky's proposal would come to be called 'tired light'- a term coined by the leading Big Bang proponent Richard Tolman.

Einstein's universe

Albert Einstein added a positive cosmological constant to his equations of general relativity to counteract the attractive effects of gravity on ordinary matter, which would otherwise cause a spatially finite universe to either collapse or expand forever.

This motivation evaporated after the proposal by the astrophysicist and Roman Catholic priest Georges Lemaître that the Universe appears to be not static, but expanding. Edwin Hubble had researched data from the observations made by astronomer Vesto Slipher to confirm a relationship between redshift and distance, which forms the basis for the modern expansion paradigm that was introduced by Lemaître. According to George Gamow this led Einstein to declare this cosmological model, and especially the introduction of the cosmological constant, his "biggest blunder".^[1]

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

R_{E}=\Lambda _{E}^{-1/2}={c \over {\sqrt {4\pi G\rho }}}.

The Einstein universe is one of Friedmann's solutions to Einstein's field equation for dust with density $\rho$ , cosmological constant $\Lambda _{E}$ , and radius of curvature $R_{E}$ . It is the only non-trivial static solution to Friedmann's equations.^{[citation needed]}

Because the Einstein universe is now known to be inherently unstable, it is no longer regarded as a viable model for the Universe. It is unstable in the sense that any change in either the value of the cosmological constant, the matter density, or the spatial curvature will result in a universe that either expands and accelerates forever or re-collapses to a big crunch.

After Einstein renounced his cosmological constant, and embraced the Friedmann-LeMaitre model of an expanding universe^{[citation needed]}, most physicists of the twentieth century assumed that the cosmological constant is zero. If so (absent some other form of dark energy), the expansion of the Universe would be decelerating. However, after Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess introduced the theory of an accelerating universe in 1998, a positive cosmological constant has been revived as a simple explanation for dark energy.

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. Second, it must explain the cosmic microwave background radiation. Third, it must have a mechanism to re-create hydrogen because, in the absence of such a mechanism, the Universe would have become nothing but black holes.

References

^ 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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 {{cosmology}}
-A '''static universe''', also referred to as a "stationary" or "infinite" or "static infinite" universe, is a [[cosmological model]] in which the universe is both spatially infinite and temporally infinite, and space is neither [[metric expansion of space|expanding]] nor contracting. Such a universe does not have [[Shape of the universe|spatial curvature]]; that is to say that it is 'flat'. A static infinite universe was first proposed by [[Giordano Bruno]].
+A '''static universe''', also referred to as a "stationary" or "infinite" or "static infinite" universe, is a [[cosmological model]] in which the Universe is both spatially infinite and temporally infinite, and space is neither [[metric expansion of space|expanding]] nor contracting. Such a universe does not have [[Shape of the universe|spatial curvature]]; that is to say that it is 'flat'. A static infinite universe was first proposed by [[Giordano Bruno]].
 In contrast to this model, [[Albert Einstein]] proposed a temporally infinite but spatially finite model as his preferred [[physical cosmology|cosmology]] in 1917, in his paper ''Cosmological Considerations in the General Theory of Relativity''.
@@ Line 9: / Line 9: @@
 Albert Einstein added a positive [[cosmological constant]] to his [[Einstein equation|equations]] of [[general relativity]] to counteract the attractive effects of [[gravity]] on ordinary matter, which would otherwise cause a spatially finite universe to either [[Big Crunch|collapse]] or expand forever.
-This motivation evaporated after the proposal by the astrophysicist and Roman Catholic priest [[Georges Lemaître]] that the universe appears to be not static, but expanding. [[Edwin Hubble]] had researched data from the observations made by astronomer [[Vesto Slipher]] to confirm a relationship between [[Hubble's Law|redshift and distance]], which forms the basis for the modern [[Metric expansion of space|expansion paradigm]] that was introduced by Lemaître. According to [[George Gamow]] this led Einstein to declare this cosmological model, and especially the introduction of the cosmological constant, his "biggest blunder".{{ref|greatestblunder}}
+This motivation evaporated after the proposal by the astrophysicist and Roman Catholic priest [[Georges Lemaître]] that the Universe appears to be not static, but expanding. [[Edwin Hubble]] had researched data from the observations made by astronomer [[Vesto Slipher]] to confirm a relationship between [[Hubble's Law|redshift and distance]], which forms the basis for the modern [[Metric expansion of space|expansion paradigm]] that was introduced by Lemaître. According to [[George Gamow]] this led Einstein to declare this cosmological model, and especially the introduction of the cosmological constant, his "biggest blunder".{{ref|greatestblunder}}
-Einstein's static universe is [[closed universe|closed]] (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive [[cosmological constant]] with value precisely <math>\Lambda_E = 4\pi G\rho/c^2</math>, where <math>G</math> is Newtonian gravitational constant, <math>\rho</math> is the energy density of the matter in the universe and <math>c</math> is the [[speed of light]].  The [[Radius of curvature (mathematics)|radius of curvature]] of space of the Einstein universe is equal to
+Einstein's static universe is [[closed universe|closed]] (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive [[cosmological constant]] with value precisely <math>\Lambda_E = 4\pi G\rho/c^2</math>, where <math>G</math> is Newtonian gravitational constant, <math>\rho</math> is the energy density of the matter in the Universe and <math>c</math> is the [[speed of light]].  The [[Radius of curvature (mathematics)|radius of curvature]] of space of the Einstein universe is equal to
 :<math>R_E = \Lambda_E^{-1/2} = {c \over \sqrt{4\pi G\rho}}.</math>
@@ Line 17: / Line 17: @@
 The Einstein universe is one of [[Robertson-Walker coordinates|Friedmann's solution]]s to Einstein's field equation for dust with density <math>\rho</math>, cosmological constant  <math>\Lambda_E</math>, and radius of curvature <math>R_E</math>. It is the only non-trivial static solution to Friedmann's equations.{{Citation needed|date=February 2010}}
-Because the Einstein universe is now known to be inherently unstable, it is no longer regarded as a viable model for the universe. It is unstable in the sense that any change in either the value of the cosmological constant, the matter density, or the spatial curvature will result in a universe that either expands and accelerates forever or re-collapses to a big crunch.
+Because the Einstein universe is now known to be inherently unstable, it is no longer regarded as a viable model for the Universe. It is unstable in the sense that any change in either the value of the cosmological constant, the matter density, or the spatial curvature will result in a universe that either expands and accelerates forever or re-collapses to a big crunch.
-After Einstein renounced his cosmological constant, and embraced the Friedmann-LeMaitre model of an expanding universe{{Citation needed|date=August 2014}}, most physicists of the twentieth century assumed that the cosmological constant is zero. If so (absent some other form of [[dark energy]]), the expansion of the universe would be decelerating. However, after [[Saul Perlmutter]], [[Brian P. Schmidt]], and [[Adam G. Riess]] introduced the theory of an [[accelerating universe]] in 1998, a positive cosmological constant has been revived as a simple explanation for [[dark energy]].
+After Einstein renounced his cosmological constant, and embraced the Friedmann-LeMaitre model of an expanding universe{{Citation needed|date=August 2014}}, most physicists of the twentieth century assumed that the cosmological constant is zero. If so (absent some other form of [[dark energy]]), the expansion of the Universe would be decelerating. However, after [[Saul Perlmutter]], [[Brian P. Schmidt]], and [[Adam G. Riess]] introduced the theory of an [[accelerating universe]] in 1998, a positive cosmological constant has been revived as a simple explanation for [[dark energy]].
 ==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]]. Second, it must explain the [[cosmic microwave background radiation]]. Third, it must have a mechanism to re-create [[hydrogen]] because, in the absence of such a mechanism, the universe would have become nothing but [[black holes]].
+In order for a static infinite universe model to be viable, it must explain three things: First, it must explain the intergalactic [[redshift]]. Second, it must explain the [[cosmic microwave background radiation]]. Third, it must have a mechanism to re-create [[hydrogen]] because, in the absence of such a mechanism, the Universe would have become nothing but [[black holes]].
 ==See also==