Inhomogeneous cosmology

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. Work towards a non-perturbative approach includes the Relativistic Zel'dovich Approximation.^[3] As of 2016, Thomas Buchert, George Ellis, Edward Kolb and their colleagues,^[4] judged that if the Universe is described by cosmic variables in a backreaction scheme that includes coarse-graining and averaging, then the question of whether dark energy is an artefact of the way of using the Einstein equation is an unanswered question.^[5]

Exact solutions

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

Averaging methods

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.

References