Realizing Scale-invariant Density Perturbations in Low-energy Effective String Theory

TL;DR

This paper explores how to generate nearly scale-invariant density perturbations in low-energy string theory by decoupling the dilaton from gravity and analyzing higher-order corrections, with implications for cosmological observations.

Contribution

It demonstrates that scale-invariant spectra can be achieved without a dilaton potential if the $( abla \, ext{phi})^4$ correction dominates, and highlights issues with Gauss-Bonnet corrections causing instabilities.

Findings

Scale-invariant scalar and tensor spectra are possible with specific corrections.

Gauss-Bonnet corrections lead to small-scale tensor instabilities.

Decoupling the dilaton is key to obtaining desired perturbation spectra.

Abstract

We discuss the realization of inflation and resulting cosmological perturbations in the low-energy effective string theory. In order to obtain nearly scale-invariant spectra of density perturbations and a suppressed tensor-to-scalar ratio, it is generally necessary that the dilaton field $\phi$ is effectively decoupled from gravity together with the existence of a slowly varying dilaton potential. We also study the effect of second-order corrections to the tree-level action which are the sum of a Gauss-Bonnet term coupled to $\phi$ and a kinetic term $(\nabla \phi)^4$. We find that it is possible to realize observationally supported spectra of scalar and tensor perturbations provided that the correction is dominated by the $(\nabla \phi)^4$ term even in the absence of the dilaton potential. When the Gauss-Bonnet term is dominant, tensor perturbations exhibit violent negative instabilities on small-scales about a de Sitter background in spite of the fact that scale-invariant scalar perturbations can be achieved.