Strength of singularities in varying constants theories

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.Comment: 5 page

Emergence of multiverse in third quantized varying constants cosmologies

Although the standard cosmological model explains most of the observed phenomena it still struggles with the problem of initial singularity. An interesting scenario in which the problem of the initial singularity is somehow circumvented was proposed in the context of string theory where the canonical quantisation procedure was additionally applied. A similar effect can be achieved in the context of the canonically quantized theory with varying speed of light and varying gravitational constant where both quantities are represented by non-minimally coupled scalar fields. Such theory contains both the pre-big-bang contracting phase and the post-big-bang expanding phase and predicts non-vanishing probability of the transition from the former to the latter phase. In this paper we quantize such a theory once again by applying the third quantization scheme and show that the resulting theory contains scenario in which the whole multiverse is created from nothing. The generated family of the universes is described by the Bose-Einstein distribution.Comment: 6 pages, 2 figure

Redshift drift in varying speed of light cosmology

We derive a redshift drift formula within the framework of varying speed of light (VSL) theory using the specific ansatz for the variability of $c(t) = c_0 a^n(t)$. We show that negative values of the parameter $n$, which correspond to diminishing value of the speed of light during the evolution of the universe, effectively rescales dust matter to become little negative pressure matter, and the cosmological constant to became phantom. Positive values of $n$ (growing $c(t)$) make VSL model to become more like Cold Dark Matter (CDM) model. Observationally, there is a distinction between the VSL model and the $\Lambda$CDM model for the admissible values of the parameter $n \sim - 10^{-5}$, though it will be rather difficult to detect by planned extremely large telescopes (E-ELT, TMT, GMT) within their accuracy.Comment: 4 pages, 1 figure, title and body changed to match a published version on redshift drift onl

Big-Rip, Sudden Future, and other exotic singularities in the universe

We discuss exotic singularities in the evolution of the universe motivated by the progress of observations in cosmology. Among them there are: Big-Rip (BR), Sudden Future Singularities (SFS), Generalized Sudden Future Singularities (GSFS), Finite Density Singularities (FD), type III, and type IV singularities. We relate some of these singularities with higher-order characteristics of expansion such as jerk and snap. We also discuss the behaviour of pointlike objects and classical strings on the approach to these singularities.Comment: 3 pages, MG11 proceedings contributio