Inhomogeneous cosmology usually means the study of structure in the Universe by means of exact solutions of Einstein's field equations (i.e. metrics) or by spatial or spacetime averaging methods. 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. 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. As of 2016, Thomas Buchert, George Ellis, Edward Kolb and their colleagues, 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.
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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.
Averaging methods
The best-known averaging approach is the scalar averaging approach, leading to the kinematical and curvature backreaction parameters; the main equations are often referred to as the set of Buchert equations.