Static universe

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In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or Euclidean.[ citation needed ][ further explanation needed ] A static infinite universe was first proposed by English astronomer Thomas Digges (1546–1595). [1]

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In contrast to this model, Albert Einstein proposed a temporally infinite but spatially finite model - static eternal universe - as his preferred cosmology during 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 American astronomers Vesto Slipher and Edwin Hubble, the Belgian astrophysicist and priest Georges Lemaître interpreted the redshift as evidence of universal expansion and thus a Big Bang, whereas Swiss astronomer 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 termed 'tired light'—a term invented by the major Big Bang proponent Richard Tolman.

The Einstein universe

During 1917, 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 static, spatially finite universe to either collapse or expand forever. [2] [3] [4] This model of the universe became known as the Einstein World or Einstein's static universe.

This motivation ended after the proposal by the astrophysicist and Roman Catholic priest Georges Lemaître that the universe seems 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 caused Einstein to declare this cosmological model, and especially the introduction of the cosmological constant, his "biggest blunder".

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 , where is Newtonian gravitational constant, is the energy density of the matter in the universe and is the speed of light. The radius of curvature of space of the Einstein universe is equal to

The Einstein universe is one of Friedmann's solutions to Einstein's field equation for dust with density , cosmological constant , and radius of curvature . It is the only non-trivial static solution to Friedmann's equations.[ 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, or the 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), 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 during 1998, a positive cosmological constant has been revived as a simple explanation for dark energy.

In 1976 Irving Segal revived the static universe in his 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. Second, it must explain the cosmic microwave background radiation. Third, it must have a mechanism to re-create matter (particularly 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. [7] [8] With the absence of such a mechanism, the universe would consist of dead objects such as black holes and black dwarfs.

See also

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In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.

<span class="mw-page-title-main">Accelerating expansion of the universe</span> Cosmological phenomenon

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther away that an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

<span class="mw-page-title-main">Hubble's law</span> 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 Earth at speeds proportional to their distance. In other words, the farther 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 toward the red end of the visible light spectrum. The discovery of Hubble's law is attributed to Edwin Hubble's work published in 1929.

<span class="mw-page-title-main">Friedmann–Lemaître–Robertson–Walker metric</span> Metric based on the exact solution of Einsteins field equations of general relativity

The Friedmann–Lemaître–Robertson–Walker metric is a metric based on an exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

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<span class="mw-page-title-main">Tired light</span> Class of hypothetical redshift mechanisms

Tired light is a class of hypothetical redshift mechanisms that was proposed as an alternative explanation for the redshift-distance relationship. These models have been proposed as alternatives to the models that involve the expansion of the universe. The concept was first proposed in 1929 by Fritz Zwicky, who suggested that if photons lost energy over time through collisions with other particles in a regular way, the more distant objects would appear redder than more nearby ones.

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<span class="mw-page-title-main">Lambda-CDM model</span> Model of Big Bang cosmology

The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

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  2. the postulated cold dark matter, denoted by CDM
  3. ordinary matter
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The flatness problem is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that small deviations from these values would have extreme effects on the appearance of the universe at the current time.

<span class="mw-page-title-main">Friedmann equations</span> Equations in physical cosmology

The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density ρ and pressure p. The equations for negative spatial curvature were given by Friedmann in 1924.

<span class="mw-page-title-main">Equation of state (cosmology)</span> Equation of state in cosmology

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<span class="mw-page-title-main">History of the Big Bang theory</span> History of a cosmological theory

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<span class="mw-page-title-main">Expansion of the universe</span> Increase in distance between parts of the universe over time

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<span class="mw-page-title-main">Deceleration parameter</span>

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<span class="mw-page-title-main">Milne model</span> Cosmological model

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<span class="mw-page-title-main">Inhomogeneous cosmology</span>

An inhomogeneous cosmology is a physical cosmological theory which, unlike the currently widely accepted cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces enough to skew our view of the Universe. When the universe began, matter was distributed homogeneously, but over billions of years, galaxies, clusters of galaxies, and superclusters have coalesced, and must, according to Einstein's theory of general relativity, warp the space-time around them. While the concordance model acknowledges this fact, it assumes that such inhomogeneities are not sufficient to affect large-scale averages of gravity in our observations. When two separate studies claimed in 1998-1999 that high redshift supernovae were further away than our calculations showed they should be, it was suggested that the expansion of the universe is accelerating, and dark energy, a repulsive energy inherent in space, was proposed to explain the acceleration. Dark energy has since become widely accepted, but it remains unexplained. Accordingly, some scientists continue to work on models that might not require dark energy. Inhomogeneous cosmology falls into this class.

Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. This concept of time avoids some issues related to relativity by being defined within a solution to the equations of general relativity widely used in cosmology.

The Einstein–de Sitter universe is a model of the universe proposed by Albert Einstein and Willem de Sitter in 1932. On first learning of Edwin Hubble's discovery of a linear relation between the redshift of the galaxies and their distance, Einstein set the cosmological constant to zero in the Friedmann equations, resulting in a model of the expanding universe known as the Friedmann–Einstein universe. In 1932, Einstein and De Sitter proposed an even simpler cosmic model by assuming a vanishing spatial curvature as well as a vanishing cosmological constant. In modern parlance, the Einstein–de Sitter universe can be described as a cosmological model for a flat matter-only Friedmann–Lemaître–Robertson–Walker metric (FLRW) universe.

Einstein's static universe, aka the Einstein universe or the Einstein static eternal universe, is a relativistic model of the universe proposed by Albert Einstein in 1917. Shortly after completing the general theory of relativity, Einstein applied his new theory of gravity to the universe as a whole. Assuming a universe that was static in time, and possessed of a uniform distribution of matter on the largest scales, Einstein was led to a finite, static universe of spherical spatial curvature.

References

  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.
  2. Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie". Sitzungs. König. Preuss. Akad.: Sitzungsb. König. Preuss. Akad. 142–152.
  3. Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). The Principle of Relativity. New York: Metheun & Co. pp. 175–188.
  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.
  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.
  6. Irving Segal (1976): Mathematical cosmology and extragalactic astronomy. Pure and Applied Mathematics Series, Vol. 68. Academic Press. 19 February 1976. ISBN   9780080873848.
  7. MacMillan, W.D. 1918. "On stellar evolution". Astrophys. J. 48: 35–49
  8. MacMillan, W.D. 1925. "Some mathematical aspects of cosmology". Science 62: 63–72, 96–99, 121–127.
  1. ^ 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."