Curvature perturbations from dimensional decoupling

TL;DR

This paper explores how dimensional decoupling in string cosmology influences scalar metric perturbations, revealing that internal dimension fluctuations act as non-adiabatic pressure variations affecting the evolution of inhomogeneities.

Contribution

It introduces a detailed analysis of scalar perturbations in a five-dimensional string cosmology with decoupled dimensions, highlighting the role of internal dimension fluctuations.

Findings

Internal dimension fluctuations contribute to non-adiabatic pressure variations.

The evolution of metric inhomogeneities is numerically modeled.

Implications for string cosmological scenarios are discussed.

Abstract

The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of two maximally symmetric Euclidean manifolds whose related scale factors evolve at a dual rate so that the expanding dimensions first accelerate and then decelerate while the internal dimensions always contract. After introducing the perturbative treatment of the inhomogeneities, a class of five-dimensional geometries is discussed in detail. Quasi-normal modes of the system are derived and the numerical solution for the evolution of the metric inhomogeneities shows that the fluctuations of the internal dimensions provide a term that can be interpreted, in analogy with the well-known four-dimensional situation, as a non-adiabatic pressure density variation. Implications of this result are discussed with particular attention to string cosmological scenarios.