Metric Perturbations in Dilaton-Driven Inflation

TL;DR

In the dilaton-driven inflation phase of string cosmology, amplified vacuum fluctuations generate both scalar and tensor metric perturbations. The authors show that tensor perturbations are straightforward, while scalar perturbations require gauge-invariant formalisms or a new off-diagonal gauge to avoid a problematic growing mode in the usual longitudinal gauge. They find that both scalar and tensor spectra are nearly Planckian, with amplitudes set by background scales like $H_1$ and $M_p$, and they predict a highly tilted relic graviton-dilaton background peaking near a maximal amplified frequency $\omega_1$. The work provides a controlled, frame- and dimensionally robust perturbative framework for pre-big-bang cosmologies, with potential observational consequences for the CMB and high-frequency gravitational backgrounds.

Abstract

We compute the spectrum of scalar and tensor metric perturbations generated, as amplified vacuum fluctuations, during an epoch of dilaton-driven inflation of the type occurring naturally in string cosmology. In the tensor case the computation is straightforward while, in the scalar case, it is made delicate by the appearance of a growing mode in the familiar longitudinal gauge. In spite of this, a reliable perturbative calculation of perturbations far outside the horizon can be performed by resorting either to appropriate gauge invariant variables, or to a new coordinate system in which the growing mode can be "gauged down". The simple outcome of this complicated analysis is that both scalar and tensor perturbations exhibit nearly Planckian spectra, whose common "temperature" is related to some very basic parameters of the string-cosmology background.