# Back-reaction

In theoretical physics, back-reaction (or backreaction) is often necessary to calculate the self-consistent behaviour of a particle or an object in an external field.

## Intuitive definition

When a particle is considered to have no mass or to have an infinitesimal charge, this can be described as saying that we deal with a probe and that back-reaction is neglected. However, a real object also carries (in general) a mass and a charge itself. These properties imply that the model of the original environment needs to be modified to reach self-consistency. For example, a particle can be described as helping to curve the space in general relativity. Taking into account the constraints implied on the model by the particle's properties – the back-reaction – is one way of reaching a more accurate model than if those constraints are ignored.

## Cosmology

In inhomogeneous cosmology, in which structure formation is taken into account in a general-relativistic model of the Universe, the term "backreaction" is used for a measure of the non-commutativity of the averaging procedure

${\displaystyle G_{\mu \nu }({\overline {g_{\alpha \beta }}})\neq {\overline {G_{\mu \nu }(g_{\alpha \beta })}}={\frac {8\pi G}{c^{4}}}{\overline {T_{\mu \nu }}}}$

(which comes from the non-linearity of Einstein field equations) and the dynamical evolution of spatial slices of space-time[1]. As of 2017, the role of backreaction in possibly leading to an alternative to dark energy is an open question of debate among cosmologists.[2][3] The existence of a homogeneity length scale can be considered to be that at which the calculations with and without backreaction give the same results. As of 2017, the existence of such a scale needs experimental confirmation.[1]

## References

1. ^ a b Buchert, Thomas (2008). "Dark Energy from structure: a status report". General Relativity and Gravitation. 40 (2–3): 467–527. arXiv:0707.2153. Bibcode:2008GReGr..40..467B. doi:10.1007/s10714-007-0554-8.
2. ^ 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. 32 (21): 215021. arXiv:1505.07800. Bibcode:2015CQGra..32u5021B. doi:10.1088/0264-9381/32/21/215021.
3. ^ 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.