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.[clarification needed]
Such models are not homogeneous[why?], but contain enough[clarification needed] 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[update], 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.
The best known[according to whom?] 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.
The best-known[according to whom?] averaging approach is the scalar averaging approach[further explanation needed], leading to the kinematical and curvature backreaction parameters; the main equations are often referred to as the set of Buchert equations.
- Krasinski, A., Inhomogeneous Cosmological Models, (1997) Cambridge UP, ISBN 0-521-48180-5
- Buchert, Thomas (2008). "Dark Energy from structure: a status report". General Relativity and Gravitation. 40: 467. arXiv: . Bibcode:2008GReGr..40..467B. doi:10.1007/s10714-007-0554-8.
- Buchert, Thomas; Nayet, Charly; Wiegand, Alexander (2013). "Lagrangian theory of structure formation in relativistic cosmology II: average properties of a generic evolution model". Physical Review D. American Physical Society. 87: 123503. arXiv: . Bibcode:2013PhRvD..87l3503B. doi:10.1103/PhysRevD.87.123503.
- Buchert, Thomas; Carfora, Mauro; Ellis, George F.R.; Kolb, Edward W.; MacCallum, Malcolm A.H.; Ostrowski, Jan J.; Räsänen, Syksy; Roukema, Boudewijn F.; Andersson, Lars; Coley, Alan A.; Wiltshire, David L. (2015-10-13). "Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?". Classical and Quantum Gravity. Institute of Physics. 32: 215021. arXiv: . Bibcode:2015CQGra..32u5021B. doi:10.1088/0264-9381/32/21/215021. Archived from the original on 2016-11-22.
- Buchert, Thomas; Carfora, Mauro; Ellis, George F.R.; Kolb, Edward W.; MacCallum, Malcolm A.H.; Ostrowski, Jan J.; Räsänen, Syksy; Roukema, Boudewijn F.; Andersson, Lars; Coley, Alan A.; Wiltshire, David L. (2016-01-20). "The Universe is inhomogeneous. Does it matter?". CQG+. Institute of Physics. Archived from the original on 2016-01-21. Retrieved 2016-01-21.