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 structure on global expansion Universe. The main question surrounding this phenomenon is whether or not it important enough lead measurable effects scale factor evolution, eventually explaining its acceleration Hubble tension. One most results subject Buchert-Ehlers theorem [T. Buchert and J. Ehlers, Astron. Astrophys. 320, 1 (1997)] stating that exactly zero when calculated using Newton's theory gravitation, which may be case in general relativity. It generally said result implies a purely relativistic effect. We will show necessarily case, sense implication does apply universe still well-described by small scales but has non-Euclidean topology. should therefore generalized account for such scenario. In heuristic calculation where we construct locally Newtonian defined topology, nonzero, meaning might nonrelativistic depending topological class our However, construction unique remains justified from limit