Cosmological Perturbations in Flux Compactifications

TL;DR

This paper analyzes the spectrum of cosmological perturbations in flux compactifications, revealing that vector and tensor modes are stable while scalar modes may have instabilities, impacting higher-dimensional cosmological models.

Contribution

It provides the first complete analysis of vector and tensor perturbations in flux compactifications, identifying potential scalar instabilities and their sources.

Findings

Vector and tensor perturbations are stable with non-negative mass squares.

Scalar perturbations exhibit potential instabilities requiring stabilization.

Form field perturbations can be a source of scalar instabilities.

Abstract

Kaluza-Klein compactifications with four-dimensional inflationary geometry combine the attractive idea of higher dimensional models with the attempt to incorporate four-dimensional early-time or late-time cosmology. We analyze the mass spectrum of cosmological perturbations around such compactifications, including the scalar, vector, and tensor sector. Whereas scalar perturbations were discussed before, the spectrum of vector and tensor perturbations is a new result of this article. Moreover, the complete analysis shows, that possible instabilities of such compactifications are restricted to the scalar sector. The mass squares of the vector and tensor perturbations are all non-negative. We discuss form fields with a non-trivial background flux in the extra space as matter degrees of freedom. They provide a source of scalar and vector perturbations in the effective four-dimensional theory. We analyze the perturbations in Freund-Rubin compactifications. Although it can only be considered as a toy model, we expect the results to qualitatively generalize to similar configurations. We find that there are two possible channels of instabilities in the scalar sector of perturbations, whose stabilization has to be addressed in any cosmological model that incorporates extra dimensions und form fields. One of the instabilities is associated with the perturbations of the form field.