Can the scale factor be rippled?

TL;DR

This paper investigates whether the cosmological scale factor can exhibit local oscillations, using two classical 1+1-dimensional models, revealing conditions under which oscillations and inhomogeneities can occur.

Contribution

It demonstrates that in specific models, the scale factor can oscillate locally and become inhomogeneous, providing insights into nonlinear gauge waves in cosmological contexts.

Findings

Existence of gauge and initial conditions for oscillating scale factors.

Homogeneous scale factor can develop inhomogeneities and nonlinear oscillations.

Oscillations can be interpreted as nonlinear gauge waves.

Abstract

We address an issue: would the cosmological scale factor be a locally oscillating quantity? This problem is examined in the framework of two classical 1+1-dimensional models: the first one is a string against a curved background, and the second one is an inhomogeneous Bianchi I model. For the string model, it is shown that there exist the gauge and the initial condition providing an oscillation of scale factor against a slowly evolving background, which is not affected by such an oscillation "at the mean". For the inhomogeneous Bianchi I model with the conformal time gauge, an initially homogeneous scale factor can become inhomogeneous and undergo the nonlinear oscillations. As is shown these nonlinear oscillations can be treated as a nonlinear gauge wave.