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We discuss minisuperspace models within the framework of varying physical constants theories including $Lambda$-term. In particular, we consider the varying speed of light (VSL) theory and varying gravitational constant theory (VG) using the specific ansatze for the variability of constants: $c(a) = c_0 a^n$ and $G(a)=G_0 a^q$. We find that most of the varying $c$ and $G$ minisuperspace potentials are of the tunneling type which allows to use WKB approximation of quantum mechanics. Using this method we show that the probability of tunneling of the universe from nothing ($a=0)$ to a Friedmann geometry with the scale factor $a_t$ is large for growing $c$ models and is strongly suppressed for diminishing $c$ models. As for $G$ varying, the probability of tunneling is large for $G$ diminishing, while it is small for $G$ increasing. In general, both varying $c$ and $G$ change the probability of tunneling in comparison to the standard matter content (cosmological term, dust, radiation) universe models.
(Abridged) Does inflation have to happen all in one go? The answer is a resounding no! All cosmological problems can be solved by a sequence of short bursts of cosmic acceleration, interrupted by short epochs of decelerated expansion. The spectrum of
In this paper, we have worked on the possibility of setting up an Bells inequality violating experiment in the context of primordial cosmology following the fundamental principles of quantum mechanics. To set up this proposal we have introduced a mod
We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find
We study the implications of the recently proposed Trans-Planckian Censorship Conjecture (TCC) for early universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a
While many aspects of general relativity have been tested, and general principles of quantum dynamics demand its quantization, there is no direct evidence for that. It has been argued that development of detectors sensitive to individual gravitons is