FLRW Universes from "Wave-Like" Cosmologies in 5D

TL;DR

This paper explores how a 4D universe embedded in a 5D bulk with wave-like metric features can reproduce standard cosmological models and predicts the growth of the extra dimension, with potential observational consequences.

Contribution

It demonstrates that wave-like 5D cosmologies can fully integrate Einstein's equations and recover FLRW universes, extending previous models with new insights on extra dimension dynamics.

Findings

The extra dimension grows if the universe accelerates.

Recovered standard FLRW cosmology from 5D wave-like models.

Estimated the change rate of the extra dimension over time.

Abstract

We consider the evolution of a 4D-universe embedded in a five-dimensional (bulk) world with a large extra dimension and a cosmological constant. The cosmology in 5D possesses "wave-like" character in the sense that the metric coefficients in the bulk are functions of the extra coordinate and time in a way similar to a pulse or traveling wave propagating along the fifth dimension. This assumption is motivated by some recent work presenting the big-bang as a higher dimensional shock wave. We show that this assumption, together with an equation of state for the effective matter quantities in 4D, allows Einstein's equations to be fully integrated. We then recover the familiar FLRW universes, on the four-dimensional hypersurfaces orthogonal to the extra dimension. Regarding the extra dimension we find that it is {\em growing} in size if the universe is speeding up its expansion. We also get an estimate for the relative change of the extra dimension over time. This estimate could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational "constant". Our results extend previous ones in the literature.