Vacuum fluctuations in axion-dilaton cosmologies

TL;DR

This work investigates vacuum fluctuations in axion-dilaton cosmologies derived from the string low-energy action, focusing on a four-dimensional FRW external space with a dilaton, axion, and modulus. By exploiting conformal-frame relations and, critically, S-duality, the authors derive both the classical backgrounds and semi-classical perturbation spectra, including invariant combinations that persist across dual backgrounds. They find the dilaton and moduli perturbations possess a steep blue spectrum with $n=4$, while the axion spectrum can be tuned by the internal-dimension expansion to be nearly scale-invariant ($n\approx1$) or as blue as $n\approx4$, with the tilt $n_\sigma=4-2r$ depending on $r=|r_\pm|=\sqrt{3-2ns^2}$. The axion frame reveals non-singular evolution for certain parameter ranges, and the late-time spectra are shown to be independent of the pre-Big Bang history within S-duality related branches, highlighting a robust pre-Big Bang imprint and potential avenues for structure formation via axions.

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.