Is backreaction in cosmology a relativistic effect? On the need for an extension of Newton’s theory to non-Euclidean topologies. (arXiv:2109.10336v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Vigneron_Q/0/1/0/all/0/1">Quentin Vigneron</a>
Cosmological backreaction corresponds to the effect of inhomogeneities of
structure on the global expansion of the Universe. The main question
surrounding this phenomenon is whether or not it could explain the recent
acceleration of the scale factor, also known as Dark Energy. One of the most
important result on this subject is the Buchert-Ehlers theorem (Buchert &
Ehlers, 1997) stating that backreaction is exactly zero when calculated using
Newton’s theory of gravitation, which may not be the case in general
relativity. It is generally said that this result implies that backreaction is
a purely relativistic effect. We will show that this is not necessarily the
case, in the sense that this implication does not apply to a universe which is
still well described by Newton’s theory on small scales but has a non-Euclidean
topology. The theorem should therefore be generalised to account for such a
scenario. In a heuristic calculation where we define a theory which is locally
Newtonian but defined on a non-Euclidean topology, we show that backreaction is
non-zero, meaning that it might be non-relativistic and might depend on the
topology of our Universe. However, this theory is yet to be justified from a
non-relativistic limit of general relativity.
Cosmological backreaction corresponds to the effect of inhomogeneities of
structure on the global expansion of the Universe. The main question
surrounding this phenomenon is whether or not it could explain the recent
acceleration of the scale factor, also known as Dark Energy. One of the most
important result on this subject is the Buchert-Ehlers theorem (Buchert &
Ehlers, 1997) stating that backreaction is exactly zero when calculated using
Newton’s theory of gravitation, which may not be the case in general
relativity. It is generally said that this result implies that backreaction is
a purely relativistic effect. We will show that this is not necessarily the
case, in the sense that this implication does not apply to a universe which is
still well described by Newton’s theory on small scales but has a non-Euclidean
topology. The theorem should therefore be generalised to account for such a
scenario. In a heuristic calculation where we define a theory which is locally
Newtonian but defined on a non-Euclidean topology, we show that backreaction is
non-zero, meaning that it might be non-relativistic and might depend on the
topology of our Universe. However, this theory is yet to be justified from a
non-relativistic limit of general relativity.
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