Inhomogeneous cosmology

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Inhomogeneous cosmology usually means the study of structure in the universe by means of exact solutions of Einstein's field equations (i.e. metrics)[1] or by spatial or spacetime averaging methods.[2] Such models are not homogeneous, but contain enough matter to be possible cosmological models, typically without dark energy, or models of cosmological structures such as voids or galaxy clusters.[1][2] In contrast, perturbation theory, which deals with small perturbations from e.g. a homogeneous metric, only holds as long as the perturbations are not too large, and N-body simulations use Newtonian gravity which is only a good approximation when speeds are low and gravitational fields are weak.

Exact solutions[edit]

The best known examples of such exact solutions are the Lemaître–Tolman metric (or LT model). Some other examples are the Szekeres metric, tSzafron metric, Stephani metric, Kantowski-Sachs metric, Barnes metric, Kustaanheimo-Qvist metric, and Senovilla metric.[1]

Averaging methods[edit]

The best-known averaging approach is the scalar averaging approach, leading to the kinematical and curvature backreaction parameters;[2] the main equations are often referred to as the set of Buchert equations.


  1. ^ a b c Krasinski, A., Inhomogeneous Cosmological Models, (1997) Cambridge UP, ISBN 0-521-48180-5
  2. ^ a b c Buchert, T., arXiv:1303.6193