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

  1. 1 2 3 Krasinski, A., Inhomogeneous Cosmological Models, (1997) Cambridge UP, ISBN 0-521-48180-5
  2. 1 2 3 Buchert, Thomas (2008). "Dark Energy from structure: a status report". General Relativity and Gravitation. 40: 467. arXiv:0707.2153Freely accessible. Bibcode:2008GReGr..40..467B. doi:10.1007/s10714-007-0554-8.
  3. ↑ 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:1303.6193Freely accessible. Bibcode:2013PhRvD..87l3503B. doi:10.1103/PhysRevD.87.123503.
  4. ↑ 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:1505.07800Freely accessible. Bibcode:2015CQGra..32u5021B. doi:10.1088/0264-9381/32/21/215021.
  5. ↑ 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 2016-01-20. Retrieved 2016-01-21.
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