Cosmological principle

See also: Friedmann-Lemaître-Robertson-Walker metric and Large-scale structure of the cosmos

Physical cosmology
Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe
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In modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics. As astronomer William Keel explains:

The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers.' This amounts to the strongly philosophical statement that the part of the Universe which we can see is a fair sample, and that the same physical laws apply throughout. In essence, this in a sense says that the Universe is knowable and is playing fair with scientists.^[1]

The cosmological principle contains three implicit qualifications and two testable consequences. The first implicit qualification is that "observers" means any observer at any location in the universe, not simply any human observer at any location on Earth: as Andrew Liddle puts it, "the cosmological principle [means that] the universe looks the same whoever and wherever you are."^[2]

The second implicit qualification is that "looks the same" does not mean physical structures necessarily, but the effects of physical laws in observable phenomena. Thus, wavelength ratios observed for different ionic species in the absorption spectra of quasi stellar objects (QSO or quasars) place a limit on any variation in the fine-structure constant to less than 1 part in 1 million out to a distance in space (and time) of z = 3 (about 6500 megaparsecs or 11.5 billion years); as the fine-structure constant is determined by the relation between the speed of light (c), Planck's constant (h) and the electron charge (e), these physical constants are constrained as well.^[1]

The third qualification, related to the second, is that variation in physical structures can be overlooked, provided this does not imperil the uniformity of conclusions drawn from observation: the sun is different from the Earth, our galaxy is different from a black hole, some galaxies advance toward rather than recede from us, and the universe has a "foamy" texture of galaxy clusters and voids, but none of these different structures appears to violate the basic laws of physics.

The two testable structural consequences of the cosmological principle are homogeneity and isotropy. Homogeneity means that the same observational evidence is available to observers at different locations in the universe ("the part of the Universe which we can see is a fair sample"). Isotropy means that the same observational evidence is available by looking in any direction in the universe ("the same physical laws apply throughout"). The principles are distinct but closely related, because a universe that appears isotropic from any two (for a spherical geometry, three) locations must also be homogeneous.

The cosmological principle is consistent with the observed isotropy of: (i) the celestial distribution of radio galaxies, which are randomly distributed across the entire sky, (ii) the large scale spatial distribution of galaxies, which form a randomly tangled web of clusters and voids up to around 400 megaparsecs in width, (iii) the isotropic distribution of observed red shift in the spectra of distant galaxies, which implies a uniform expansion of space or Hubble flow in all directions, and (iv) the cosmic microwave background radiation, the relic radiation released by the expansion and cooling of the early universe, which is constant in all directions to within 1 part in 100,000.^[3][4] For example, deep sky galaxy surveys, such as the Sloan Digital Sky Survey^[5] or the 2dF Galaxy Redshift Survey,^[6] combine line of sight galaxy positions with red shift data to produce three dimensional maps of galaxy clustering across an estimated area over 4 billion light years wide (a red shift radius of z > 0.20); statistical tests applied to these maps confirm that isotropy applies to different viewpoints within them.^[7] The cosmic microwave background is the same from all parts of the sky, yet in cosmological theory these must have originated in completely different parts of the early universe.^[8]

The cosmological principle is first clearly asserted in the Philosophiæ Naturalis Principia Mathematica (1687) of Isaac Newton. In contrast to earlier classical or medieval cosmologies, in which Earth rested at the center of Universe, Newton conceptualized the earth as a sphere in orbital motion around the sun within an empty space that extended uniformly in all directions to immeasurably large distances. He then showed, through a series of mathematical proofs on detailed observational data of the motions of planets and comets, that their motions could be explained by a single principle of "universal gravitation" that applied as well to the orbits of the Galilean moons around Jupiter, the moon around the earth, the earth around the sun, and to falling bodies on earth. That is, he asserted the equivalent material nature of all bodies within the solar system, the identical nature of the sun and distant stars ("the light of the fixed stars is of the same nature with the light of the sun, ... and lest the systems of the fixed stars should, by their gravity, fall on each other, [God] hath placed those systems at immense distances from one another"), and thus the uniform extension of the physical laws of motion to a great distance beyond the observational location of earth itself.

Implications

The cosmological principle represents both the principle on which cosmological theory and observation can proceed and a "null" hypothesis of uniformity that is an area of active research inquiry.^[9] Many important advances in astronomy and cosmology, and the formulation of new cosmological theories, have occurred through the resolution of apparent violations of the cosmological principle. For example, the original discovery that far galaxies appeared to have higher spectral red shifts than near galaxies (an apparent violation of homogeneity) led to the discovery of Hubble flow, the metric expansion of space that occurs equally in all locations (restoring homogeneity).

The universe is now described as having a history, starting with the Big Bang and proceeding through distinct epochs of stellar and galaxy formation. Because this history is currently described (back to the first fraction of a second after the origin) almost entirely in terms of known physical processes and particle physics, the cosmological principle is extended to assert the homogeneity of cosmological evolution across the anisotropy of time:

… all points in space ought to experience the same physical development, correlated in time in such a way that all points at a certain distance from an observer appear to be at the same stage of development. In that sense, all spatial conditions in the Universe must appear to be homogeneous and isotropic to an observer at all times in the future and in the past.^[10]

That is, earlier times are identical to the "distance from the observer" in spacetime, which is assessed as the red shift of the light arriving from the observed celestial object: the cosmological principle is preserved because the same sequence of evolution is observed in all directions from earth, and is inferred to be identical to the sequence that would be observed from any other location in the universe.

Observations of distant galaxies reveal that as the distance from the Earth increases, the density of galaxies rises and their "metal" content (relative proportion of chemical elements heavier than lithium) declines.^[11] To account for this, scientists applying the cosmological principle suggest that heavier elements were not created in the "Big Bang" but were produced by nucleosynthesis in giant stars and expelled across a series of supernovae explosions and new star formation from the supernovae remnants, which means heavier elements would accumulate over time. The hypothesis of cosmological history is also supported by the fact that many more fragmentary, interacting and unusually shaped galaxies are found at high red shifts (earlier time) than in the local universe (recent time), suggesting evolution in galaxy structure as well.

A related implication of the cosmological principle is that the largest discrete structures in the universe are in mechanical equilibrium. Homogeneity and isotropy of matter at the largest scales would suggest that the largest discrete structures are parts of a single indiscrete form, like the crumbs which make up the interior of a cake. At extreme cosmological distances, the property of mechanical equilibrium in surfaces lateral to the line of sight can be empirically tested; however, under the assumption of the cosmological principle, it cannot be detected parallel to the line of sight (see timeline of the universe).

Cosmologists agree that in accordance with observations of distant galaxies, a universe must be non-static if it follows the cosmological principle. In 1923, Alexander Friedmann set out a variant of Einstein's equations of general relativity that describe the dynamics of a homogeneous isotropic universe.^[12][13] Independently, Georges Lemaître derived in 1927 the equations of an expanding universe from the General Relativity equations.^[14] Thus, a non-static universe is also implied, independent of observations of distant galaxies, as the result of applying the cosmological principle to general relativity.

See also

• Copernican principle
• Friedmann-Lemaître-Robertson-Walker metric
• Large scale structure of the cosmos
• Metric expansion of space
• Perfect cosmological principle
• Redshift
• Background independence

References

1. ^ ^{a b} William C. Keel (2007). The Road to Galaxy Formation (2nd ed.). Springer-Praxis. ISBN 978-3-540-72534-3. . p. 2.
2. ^ Andrew Liddle (2003). An Introduction to Modern Cosmology (2nd ed.). John Wiley & Sons. ISBN 978-0-470-84835-7. . p. 2.
3. ^ David Schramm & RV Wagoner (1996). "What can deuterium tell us?". In DN Schramm. The Big Bang and Other Explosions in Nuclear and Particle Astrophysics (1974 "Physics Today" article ed.). World Scientific. p. 98. ISBN 9810220243. http://books.google.com/?id=TtrxQGjYqU8C&pg=PA98. 
4. ^ S Blondin et al. (2008). "Time dilation in type Ia supernova spectra at high redshift". Astrophys J 682 (2): 724–736. arXiv:0804.3595. Bibcode 2008ApJ...682..724B. doi:10.1086/589568. 
5. ^ "The Sloan Digital Sky Survey". http://www.sdss.org/. Retrieved January 9, 2010. 
6. ^ "The 2dF Galaxy Redshift Survey Final Release Data". http://www.mso.anu.edu.au/2dFGRS/. Retrieved January 9, 2010. 
7. ^ William Keel. "Large Scale Structure". http://astronomy.ua.edu/keel/galaxies/largescale.html. Retrieved January 9, 2010. 
8. ^ George Ellis & Mauro Carfora (2000). Flat and Curved Space-times. Oxford University Press. ISBN 0198506562. http://books.google.com/?id=Hos31wty5WIC&pg=PA298. 
9. ^ GFR Ellis (1975). "Cosmology and verifiability". Royal Astronomical Society, Quarterly Journal 16: 245–264. Bibcode 1975QJRAS..16..245E. 
10. ^ Klaus Mainzer and J Eisinger (2002). The Little Book of Time. Springer. ISBN 0387952888. http://books.google.com/?id=wX111YnexSUC&pg=PA55. . P. 55.
11. ^ Image:CMB Timeline75.jpg - NASA (public domain image)
12. ^ Alexander Friedmann (1923). Die Welt als Raum und Zeit (The World as Space and Time). Ostwalds Klassiker der exakten Wissenschaften. ISBN 3817132875. http://www.worldcat.org/oclc/248202523&referer=brief_results. .
13. ^ Ėduard Abramovich Tropp, Viktor Ya. Frenkel, Artur Davidovich Chernin (1993). Alexander A. Friedmann: The Man who Made the Universe Expand. Cambridge University Press. p. 219. ISBN 0521384702. http://books.google.com/?id=0DPC4a0CSq4C&pg=PA219. 
14. ^ Lemaître, Georges (1927). "Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques". Annales de la Société Scientifique de Bruxelles A47: 49–56. Bibcode 1927ASSB...47...49L  translated by A. S. Eddington: Lemaître, Georges (1931). "Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulæ". Monthly Notices of the Royal Astronomical Society 91: 483–490. Bibcode 1931MNRAS..91..483L