# Back-reaction

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

## Intuitive definition

When a particle is considered to have no mass or to have an [infinitesimal](/source/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](/source/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](/source/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

- 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](/source/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. Buchert, Thomas (2008). "Dark Energy from structure: a status report". *[General Relativity and Gravitation](/source/General_Relativity_and_Gravitation)*. **40** (2–3): 467–527. [arXiv:0707.2153](https://arxiv.org/abs/0707.2153). [Bibcode:2008GReGr..40..467B](https://ui.adsabs.harvard.edu/abs/2008GReGr..40..467B). [doi:10.1007/s10714-007-0554-8](https://doi.org/10.1007/s10714-007-0554-8). [S2CID 17281664](https://api.semanticscholar.org/CorpusID:17281664)

1. 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](/source/Classical_and_Quantum_Gravity)*. **32** (21). [arXiv:1505.07800](https://arxiv.org/abs/1505.07800). [Bibcode:2015CQGra..32u5021B](https://ui.adsabs.harvard.edu/abs/2015CQGra..32u5021B). [doi:10.1088/0264-9381/32/21/215021](https://doi.org/10.1088/0264-9381/32/21/215021). [S2CID 51693570](https://api.semanticscholar.org/CorpusID:51693570)

1. 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?"](http://cqgplus.com/2016/01/20/the-universe-is-inhomogeneous-does-it-matter/). *CQG+*. [Institute of Physics](/source/Institute_of_Physics). [Archived](https://web.archive.org/web/20160123220203/http://cqgplus.com/2016/01/20/the-universe-is-inhomogeneous-does-it-matter/) 2016-01-23 at the Wayback Machine. Retrieved 2016-01-21.

## External links

Shaun Hotchkiss (1 July 2015). ["The Trenches of Discovery: Cosmological Backreaction"](http://trenchesofdiscovery.blogspot.com.au/2015/07/cosmological-backreaction.html). Retrieved 23 January 2016.

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