Cosmological perturbation spectra from SL(4,R)-invariant effective actions

TL;DR

This paper derives cosmological perturbation spectra from SL(4,R)-invariant effective actions, showing conditions under which axion fields can seed cosmic anisotropies, relevant for understanding early universe fluctuations.

Contribution

It provides the first general solutions for linear axion perturbations in SL(4,R)-invariant cosmological models and analyzes their spectral properties.

Findings

All axion spectra can have positive tilt in certain parameter regimes.

Spectra derived from vacuum fluctuations can serve as seeds for cosmic anisotropies.

The work extends previous models to higher symmetry groups like SL(4,R).

Abstract

We investigate four-dimensional cosmological vacuum solutions derived from an effective action invariant under global SL(n,R) transformations. We find the general solutions for linear axion field perturbations about homogeneous dilaton-moduli-vacuum solutions for an SL(4,R)-invariant action and find the spectrum of super-horizon perturbations resulting from vacuum fluctuations in a pre big bang scenario. We show that for SL(n,R)-invariant actions with n>3 there exists a regime of parameter space of non-zero measure where all the axion field spectra have positive spectral tilt, as required if light axion fields are to provide a seed for anisotropies in the microwave background and large-scale structure in the universe.