See also: structure formation, cosmic microwave background radiation, general relativity, and classical mechanics
In physical cosmology, cosmological perturbation theory[1][2][3][4][5] is the theory by which the evolution of structure is understood in the Big Bang model. Cosmological perturbation theory may be broken into two categories: Newtonian or general relativistic. Each case uses its governing equations to compute gravitational and pressure forces which cause small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. Both cases apply only to situations where the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used. When deciding whether to use general relativity for perturbation theory, note that Newtonian physics is only applicable in some cases such as for scales smaller than the Hubble horizon, where spacetime is sufficiently flat, and for which speeds are non-relativistic.
Because of the gauge invariance of general relativity, the correct formulation of cosmological perturbation theory is subtle.
In particular, when describing an inhomogeneous spacetime, there is often not a preferred coordinate choice. There are currently two distinct approaches to perturbation theory in classical general relativity:
gauge-invariant perturbation theory based on foliating a space-time with hyper-surfaces, and
1+3 covariant gauge-invariant perturbation theory based on threading a space-time with frames.
^Fry, J. N. (April 1984). "The Galaxy correlation hierarchy in perturbation theory". The Astrophysical Journal. 279: 499. Bibcode:1984ApJ...279..499F. doi:10.1086/161913.
^Bharadwaj, Somnath (June 1994). "Perturbative growth of cosmological clustering. I: Formalism". The Astrophysical Journal. 428: 419. Bibcode:1994ApJ...428..419B. doi:10.1086/174254. ISSN 0004-637X.
^Bharadwaj, Somnath (March 1996). "Perturbative Growth of Cosmological Clustering. II. The Two-Point Correlation". The Astrophysical Journal. 460: 28–50. arXiv:astro-ph/9511085. Bibcode:1996ApJ...460...28B. doi:10.1086/176950. S2CID 17179734.
^Bharadwaj, Somnath (20 November 1996). "The Evolution of Correlation Functions in the Zeldovich Approximation and Its Implications for the Validity of Perturbation Theory". The Astrophysical Journal. 472 (1): 1–13. arXiv:astro-ph/9606121. Bibcode:1996ApJ...472....1B. doi:10.1086/178036.
^Dodelson, Scott; Schmidt, Fabian (2020). Modern Cosmology (2 ed.). Academic Press. Bibcode:2020moco.book.....D. doi:10.1016/C2017-0-01943-2. ISBN 978-0-12-815948-4. S2CID 241570171.
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