The oscillatory anisotropy in the spatially flat cosmological models

TL;DR

This paper studies the oscillatory behavior of anisotropy in Bianchi-I cosmological models, providing new theoretical insights into their evolution, solutions, and conditions for isotropization or anisotropization over cosmic time.

Contribution

It offers a simplified Einstein's equations approach, proves general oscillation results, and derives classes of exact solutions for anisotropic cosmologies.

Findings

Oscillations of anisotropy can occur without violating energy conditions.

Identifies conditions favoring isotropization or anisotropization.

Provides a framework for deriving exact solutions in anisotropic models.

Abstract

In this manuscript, we investigate the oscillatory behaviour of the anisotropy in the diagonal Bianchi-I spacetimes. Our starting point is a simplification of Einstein's equations using only observable or physical variables. As a consequence, we are able to: (a) Prove general results concerning the existence of oscillations of the anisotropy in the primordial and the late-time universe. For instance, in the expanding scenario, we show that a past weakly mixmaster behaviour (oscillations as we approach the Kasner solutions) might appear even with no violation of the usual energy conditions, while in the future, the pulsation (oscillations around isotropic solutions) seems to be most favored; (b) Determine a large scheme for deriving classes of physically motivated exact solutions, and we give some (including the general barotropic perfect fluid and the magnetic one); (c) Understand the physical conditions for the occurrence of the isotropization or anisotropization during the cosmological evolution; (d) Understand how anisotropy and energy density are converted one into another. In particular, we call attention to the presence of a residue in the energy density in a late-time isotropic universe coming from its past anisotropic behaviour.