Is backreaction in cosmology a relativistic effect? On the need for an
  extension of Newton's theory to non-Euclidean topologies
  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 is important enough to lead to
measurable effects on the scale factor evolution eventually explaining its
acceleration or the Hubble tension. 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 construct 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 depending on the topological class of our
Universe. However, that construction is not unique and remains to be justified
from a non-relativistic limit of general relativity.
