Anisotropic Multiverse with Varying $c$, $G$ and Study of Thermodynamics

TL;DR

This paper explores an anisotropic multiverse model with varying fundamental constants $c$ and $G$, analyzing singularities, thermodynamics, and entropy behaviors to understand the universe's evolution and thermodynamic properties.

Contribution

It introduces a novel anisotropic multiverse framework with varying $c$ and $G$, analyzing singularities and thermodynamics in this context.

Findings

Conditions for different singularities are derived.

Total entropy of the multiverse is computed for various models.

The nature of the multiverse is characterized when total entropy is constant.

Abstract

We assume the anisotropic model of the Universe in the framework of varying speed of light $c$ and varying gravitational constant $G$ theories and study different types of singularities. For the singularity models, we write the scale factors in terms of cosmic time and found some conditions for possible singularities. For future singularities, we assume the forms of varying speed of light and varying gravitational constant. For regularizing big bang singularity, we assume two forms of scale factors: sine model and tangent model. For both the models, we examine the validity of null energy condition and strong energy condition. Start from the first law of thermodynamics, we study the thermodynamic behaviours of $n$ number of Universes (i.e., Multiverse) for (i) varying $c$, (ii) varying $G$ and (iii) both varying $c$ and $G$ models. We found the total entropies for all the cases in the anisotropic Multiverse model. We also found the nature of the Multiverse if total entropy is constant.