Do isotropic tidal forces imply isotropic cosmic expansion?

Abstract

AbstractWe 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 a strong-like energy condition to hold, a characteristic which becomes dominant in the radiation era and even more stringent under a stiff matter regime. This is a rather counter-intuitive behavior that shows us how, from the conceptual viewpoint, the Hubble parameter tends to anisotropize even when the universe is dominated by isotropic gravitational forces and usual physical conditions. We introduce the parameterb, which measures the relative variation in the magnitudes of the Hubble anisotropy against the scale factor, to show that mechanisms violating such an energy condition can compensate for this anisotropy increase. We also discuss if there is theoretical support for the existence of observational Hubble anisotropy in the late-time universe.