Observational backreaction in discrete black holes lattice cosmological models

Abstract

The optical properties encoded in the distance modulus are studied along curves exhibiting local rotational symmetry for a class of topologically closed inhomogeneous cosmological models whose mass content is discretized and modeled through Schwarzschild-like black holes arranged on a 3-sphere. The calculations are based on the Sachs formalism. It is shown that these models may challenge the current concordance model in its use of the distance modulus data of type Ia supernovae, given that our models do not violate any energy condition. It is proved that this result relies only on the symmetry properties considered, and not on the way in which the mass is discretized. The models with different number of sources are then compared among themselves and with a closed Friedmann-Lemaitre-Robertson-Walker model with the same total mass content introducing a compactness parameter. The analysis shows that observational backreaction occurs in this model because increasing the number of sources the optical properties of a universe with a continuous matter distribution are not recovered. Our models are shown to exhibit a non-trivial relationship between kinematical, dynamical and observational backreactions, the kinematical one being absent while the latter two are present. In our models, the electric part of the Weyl tensor contributes to the luminosity distance by affecting the evolution of the scale factor, while the magnetic part has a more indirect role by only affecting the evolution of the electric part.

Discrete Black Holes

“…Numerical computations based on lattices also play an important role in cosmology. Here, the link to black holes is present in the approach of black hole lattices [7,8] allowing to build large scale cosmological models from sets of discrete matter sources.…”