Vacuum fluctuations in axion-dilaton cosmologies

TL;DR

This paper investigates axion-dilaton cosmologies from string theory, analyzing classical solutions and deriving invariant perturbation spectra, revealing conditions for scale-invariance and non-singular metrics.

Contribution

It introduces S-duality invariant perturbation solutions in axion-dilaton cosmologies, highlighting conditions for scale-invariant spectra and non-singular metrics in the pre-Big Bang scenario.

Findings

Dilaton and moduli fields have steep blue spectra with n=4.

Axion spectrum varies with internal dimension expansion, allowing n=1.

Non-singular metrics occur for spectra with n<1.

Abstract

We study axion-dilaton cosmologies derived from the low-energy string effective action. We present the classical homogeneous Friedmann-Robertson-Walker solutions and derive the semi-classical perturbation spectra in the dilaton, axion and moduli fields in the pre-Big Bang scenario. By constructing the unique S-duality invariant field perturbations for the axion and dilaton fields we derive S-duality invariant solutions, valid when the axion field is time-dependent as well as in a dilaton-vacuum cosmology. Whereas the dilaton and moduli fields have steep blue perturbation spectra (with spectral index n=4) we find that the axion spectrum depends upon the expansion rate of the internal dimensions (0.54<n<4) which allows scale-invariant (n=1) spectra. We note that for n<1 the metric is non-singular in the conformal frame in which the axion is minimally coupled.