http://arxiv.org/abs/2212.00675
In the first paper of this series, we showed that Einstein’s equation is incompatible with the non-relativistic limit in non-Euclidean topologies, i.e. for which the covering space is not $\mathbb{E}^3$. We proposed and motivated a modification of that equation such that this limit is possible. The new equation features an additional `topological term’ related to a second non-dynamical, reference, metric. In this second paper, we analyse the consequences for cosmology of this modification of Einstein’s equation. First, we show that the expansion laws do not feature anymore the curvature parameter (i.e. $\Omega = 1, \ \forall \Omega_K$). This is valid for the exact homogeneous and isotropic solution of the bi-metric theory, and for a general (inhomogeneous) solution in the non-relativistic limit. Second, we show that the weak field equations have the same number of free parameters as for the $k\Lambda$CDM model, i.e. with curvature, the differences being the disappearance of the coupling terms with that curvature in the scalar mode equations. Therefore, in our cosmological model, spatial curvature has smaller effects on the dynamics than in the $k\Lambda$CDM model; the effect remains essentially geometrical. Accordingly, the main observational difference we may expect between our model and the $k\Lambda$CDM model is a non-negligible spatial curvature inferred from cosmological data. This is particularly interesting in the context of a rising debate on the value of $\Omega_K$ and increasing observational tensions.
Q. Vigneron
Fri, 2 Dec 22
25/81
Comments: 22 pages, 1 figure, 1 table, submitted to Classical and Quantum Gravity