Spatially flat universes with isotropic tidal forces

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 in 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.