Cosmological perturbation theory

In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the big bang model. It uses general relativity to compute the gravitational forces causing small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. It only applies to situations in which 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.

Because of the gauge invariance of general relativity, the correct formulation of cosmological perturbation theory is subtle. There are currently two distinct approaches to perturbation theory in classical general relativity:

The gauge-invariant perturbation theory is based on developments by Bardeen (1980), Kodama and Sasaki (1984) building on the work of Lifshitz (1946). This is the standard approach to perturbation theory of general relativity for cosmology. This approach is widely used for the computation of anisotropies in the cosmic microwave background radiation as part of the physical cosmology program and focuses on predictions arising from linearisations that preserve gauge invariance with respect to Friedmann-Lemaître-Robertson-Walker (FLRW) models. This approach draws heavily on the use of Newtonian like analogue and usually has as it starting point the FRW background around which perturbations are developed. The approach is non-local and coordinate dependent but gauge invariant as the resulting linear framework is built from a specified family of background hyper-surfaces which are linked by gauge preserving mappings to foliate the space-time. Although intuitive this approach does not deal well with the nonlinearities natural to general relativity.

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