Some Developments in Newtonian Cosmology

Backreaction: directions of progress

“…The small-velocity, weak field limit of general relativity is not Newtonian gravity, as demonstrated by the existence of Newtonian solutions which are not the limit of any general relativity solution [27,56]. Rather, it is a theory with new degrees of freedom and additional constraints compared to Newtonian gravity [27,[57][58][59][60]. The formulation of this limit of general relativity in the cosmological setting with non-linear perturbations is an open issue.…”

Light propagation and the average expansion rate in near-FRW universes

“…However, an essential feature of the usual post-Newtonian scheme is that the system is finite and isolated, which is not the case in cosmology. In fact, Newtonian gravity has a well-defined initial value problem only for isolated systems, periodic boundary conditions or fractal distributions with vanishing mean density [31,35,36,[76][77][78]. Related to this, the non-relativistic limit of taking the speed of light to infinity is singular, so solutions of the limiting Newtonian equations are in general not limits of solutions of the relativistic equations [32,36].…”

“…In a semirealistic model, the observed timescale and the order of magnitude of the change in the expansion rate emerge from the physics of structure formation [22,23], but there is no fully realistic calculation yet. If backreaction is significant (and the universe is statistically homogeneous and isotropic with a homogeneity scale smaller than the horizon), this has to be due to non-Newtonian aspects of gravity [11,12,14,15,22,[24][25][26][27][28] which are related to the difference between Newtonian gravity and the weak field, small velocity limit of general relativity [29][30][31][32][33][34][35][36].…”

Applicability of the linearly perturbed FRW metric and Newtonian cosmology

“…However, there is no fully realistic calculation yet, and whether backreaction is important in the real universe remains an open question. The difference between Newtonian gravity and the weak field, small velocity limit of general relativity [22][23][24][25][26][27][28][29] plays an important part in the problem. Therefore, quantifying the importance of the growth of structures on the average expansion rate requires treating a statistically homogeneous and isotropic but locally complicated non-linear system in general relativity.…”