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

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 $ϕ$ 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 $ϕ$ and a kinetic term $(\nabla ϕ)^4$. We find that it is possible to realize observationally supported spectra of scalar and tensor perturbations provided that the correction is dominated by the $(\nabla ϕ)^4$ 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.

13 pages; v2: minor corrections, refs. added, version to appear in PRD