Spatially flat universes with isotropic tidal forces

TL;DR

This paper explores the evolution of spatially flat universes under isotropic tidal forces, revealing conditions under which anisotropies grow and how inflationary periods can preserve isotropy, challenging the stability of FLRW models.

Contribution

It introduces a parameter to measure anisotropy evolution and demonstrates the instability of FLRW universes under certain conditions, highlighting the role of inflation in maintaining isotropy.

Findings

Anisotropies tend to grow at late times under strong energy conditions.

Inflationary periods help keep anisotropies small, supporting the cosmic no-hair theorem.

FLRW universes are shown to be unstable without inflation.

Abstract

We investigate the dynamics of the spatially flat universes submitted to isotropic tidal forces and adiabatic expansion under Einstein's equations. Surprisingly, the tendency to a high Hubble anisotropy at late times starts to appear as far as we assume the strong energy condition, a characteristic which becomes dominant in the radiation era and even more stringent under a stiff matter regime. We introduce the parameter b which measures the relative change in the magnitudes of the Hubble anisotropy and the scale factor and use it to show that the anisotropies must be kept small as long as we assume the Universe has passed through an inflationary period, in accordance with the cosmic no-hair theorem. Hence, we have a class of models that shows us a simple and straightforward way the instability of the FLRW universes, the furtiveness of the isotropy concept, and how they can still be consistent with the standard model of Cosmology as far as we assume the occurrence of an inflationary early period.