Anisotropic Bianchi-I cosmological model in non-conservative unimodular gravity

TL;DR

This paper develops an anisotropic Bianchi-I cosmological model within non-conservative unimodular gravity, analyzing its solutions, dependence on an equation of state parameter, and consistency with observed universe properties.

Contribution

It introduces a novel anisotropic Bianchi-I model in non-conservative unimodular gravity with conditions to resolve underdetermination and explores its cosmological implications.

Findings

Vacuum solutions analogous to Kasner solutions.

Physically interesting case with negative (ρ+p) indicating super-accelerated universe.

Model consistent with observed universe age and isotropization over time.

Abstract

In this article, we propose an anisotropic Bianchi-I type cosmological model in non-conservative Unimodular Gravity ($\mathrm{NUG}$). We show that simply using the Bianchi-I type metric does not resolve a striking characteristic of the field equations in $\mathrm{NUG}$: their underdetermination. This fact led us to implement extra conditions on the combination $\left(\rho+p\right)$ and, consequently, obtain a consistent background cosmological analysis. In the vacuum case, we obtain an analogy between the Kasner solutions and the equations in $\mathrm{NUG}$. We also propose a new analysis of a non-homogeneous equation of state, the combination $\left(\rho+p\right)=l$. We identify that the cosmological dynamics are strictly dependent on the value of the constant $l$. The physically interesting case is at the value $l<0$, which seems to indicate a super-accelerated, ghost-like universe. This case still requires a more detailed analysis, for example, from a thermodynamic point of view, keeping in mind that $\left(\rho+p\right)$ may be interpreted as enthalpy of the system. For the cases $\left(\rho+p\right)\propto a^{-3}$ and $\left(\rho+p\right) \propto a^{-4}$, we obtain a description consistent with the anisotropic cosmological model described by $\mathrm{GR}$. In all cases analyzed, a small value for the anisotropic parameter $\Omega_{A}$ (on the order of $10^{-2}$) is required in order to have agreement, for example, with the age of the universe to be approximately $12-14\, \mathrm{Gyr}$, agreeing with the age of globular clusters. As the universe expands an isotropization is verified, with the anistropies going to zero asymptotically, similarly with what happens in an anistropic cosmological model based on $\mathrm{GR}$.