We review the variety of new singularities in homogeneous and isotropic FRW cosmology which differ from standard Big-Bang and Big-Crunch singularities and suggest how the nature of these singularities can be influenced by the varying fundamental constants.
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 Krolak. 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.
We show that black holes with a Schwarzschild radius of the order of the electroweak scale may act as seeds for the baryon number violation within the Standard model via sphaleron transitions. The corresponding rate is faster than the one in the pure
vacuum and baryon number violation around black holes can take place during the evolution of the universe after the electroweak phase transition. We show however that this does not pose any threat for a pre-existing baryon asymmetry in the universe.
Gravitational waves detected from well-localized inspiraling binaries would allow to determine, directly and independently, both binary luminosity and redshift. In this case, such systems could behave as standard candles providing an excellent probe
of cosmic distances up to $z <0.1$ and thus complementing other indicators of cosmological distance ladder.
We derive a luminosity distance formula for the varying speed of light (VSL) theory which involves higher order characteristics of expansion such as jerk, snap and lerk which can test the impact of varying $c$ onto the evolution of the universe. We s
how that the effect of varying $c$ is possible to be isolated due to the relations connecting observational parameters already by measuring the second-order term in redshift $z$ unless there is a redundancy between the curvature and an exotic fluid of cosmic strings scaling the same way as the curvature.
Various classes of exotic singularity models have been studied as possible mimic models for the observed recent acceleration of the universe. Here we further study one of these classes and, under the assumption that they are phenomenological toy mode
ls for the behavior of an underlying scalar field which also couples to the electromagnetic sector of the theory, obtain the corresponding behavior of the fine-structure constant $alpha$ for particular choices of model parameters that have been previously shown to be in reasonable agreement with cosmological observations. We then compare this predicted behavior with available measurements of $alpha$, thus constraining this putative coupling to electromagnetism. We find that values of the coupling which would provide a good fit to spectroscopic measurements of $alpha$ are in more than three-sigma tension with local atomic clock bounds. Future measurements by ESPRESSO and ELT-HIRES will provide a definitive test of these models.