Strength of singularities in varying constants theories

TL;DR

This paper investigates the nature of singularities in a bimetric cosmological model where two metrics define matter and gravitational structures, revealing conditions under which singularities become physically strong due to variations in the effective gravitational constant and speed of light.

Contribution

It introduces a specific bimetric framework with conformally related metrics and analyzes the strength of cosmological singularities within this model, linking them to the behavior of a time-dependent scaling factor.

Findings

Vanishing or diverging scaling factor can lead to strong singularities.

Singularities may have infinite energy density and pressure.

The model connects singularity strength to variations in fundamental constants.

Abstract

In this paper we consider a specific type of the bimetric theory of gravitation with the two different metrics introduced in the cosmological frame. Both metrics respect all the symmetries of the standard FLRW solution and contain conformally related spatial parts. One of the metric is assumed to describe the causal structure for the matter. Another metric defines the causal structure for the gravitational interactions. A crucial point is that the spatial part of the metric describing gravity is given by the spatial part of the matter metric confromally rescaled by a time-dependent factor $\alpha$ which, as it turns out, can be linked to the effective gravitational constant and the effective speed of light. In the context of such a bimetric framework we examine the strength of some singular cosmological scenarios in the sense of the criteria introduced by Tipler and Kr\'olak. In particular, we show that for the nonsingular scale factor associated with the matter metric, both the vanishing or blowing up of the factor $\alpha$ for some particular moment of the cosmic expansion may lead to a strong singularity with infinite value of the energy density and infinite value of the pressure.