On the superstrings-induced four-dimensional gravity, and its applications to cosmology

TL;DR

This paper reviews superstring-induced four-dimensional gravity terms, explores their impact on cosmological evolution, and identifies specific quartic curvature terms necessary for consistent, stable inflationary solutions without singularities.

Contribution

It proposes generalized Friedmann equations incorporating superstring effects, finds exact inflationary solutions, and clarifies the form of quartic curvature terms needed in the effective action.

Findings

Existence of non-singular de Sitter inflationary solutions

Naive quartic terms like Bel-Robinson tensor squared are ruled out

Extra Ricci tensor-dependent quartic terms are necessary

Abstract

We review the status of the fourth-order (quartic in the spacetime curvature) terms induced by superstrings/M-theory (compactified on a warped torus) in the leading order with respect to the Regge slope parameter, and study their (non-perturbative) impact on the evolution of the Hubble scale in the context of the four-dimensional FRW cosmology. After taking into account the quantum ambiguities in the definition of the off-shell superstring effective action, we propose the generalized Friedmann equations, find the existence of their (de Sitter) exact inflationary solutions without a spacetime singularity, and constrain the ambiguities by demanding stability and the scale factor duality invariance of our solutions. The most naive (Bel-Robinson tensor squared) quartic terms are ruled out, thus giving the evidence for the necessity of extra quartic (Ricci tensor-dependent) terms in the off-shell gravitational effective action for superstrings. Our methods are generalizable to the higher orders in the spacetime curvature.