Inhomogeneous cosmology

In cosmology and general relativity, Inhomogeneous cosmology is the study of the Universe that takes structure formation (galaxies, galaxy clusters, the cosmic web) into account.

This usually includes 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]

Homogeneity

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]

Perturbative approach

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.

Non-perturbative approach

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 backreaction and mean 3-Ricci curvature functionals;^[2] the main equations are often referred to as the set of Buchert equations.

References