On compatibility of string effective action with an accelerating universe

TL;DR

This paper investigates how string theory corrections, involving moduli and dilaton fields coupled with the Gauss-Bonnet invariant, can produce cosmic acceleration and inflation, with implications for the universe's expansion phases and observational constraints.

Contribution

It introduces a model with moduli-dependent one-loop corrections to string effective action that can explain both standard and non-standard inflationary behaviors and transition between acceleration phases.

Findings

Model allows transition between deceleration and acceleration.

Positive coupling coefficient leads to standard inflation ($w \,\geq\, -1$).

Negative coupling coefficient can produce super-acceleration ($w < -1$).

Abstract

In this paper, we fully investigate the cosmological effects of the moduli dependent one-loop corrections to the gravitational couplings of the string effective action to explain the cosmic acceleration problem in early (and/or late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant multiplied by universal non-trivial functions of the common modulus $\sigma$ and the dilaton $\phi$. The model exhibits several features of cosmological interest, including the transition between deceleration and acceleration phases. By considering some phenomenologically motivated ansatzs for one of the scalars and/or the scale factor (of the universe), we also construct a number of interesting inflationary potentials. In all examples under consideration, we find that the model leads only to a standard inflation ($w \geq -1$) when the numerical coefficient $\delta$ associated with modulus-GB coupling is positive, while the model can lead also to a non-standard inflation ($w<-1$), if $\delta$ is negative. In the absence of (or trivial) coupling between the GB term and the scalars, there is no crossing between the $w< -1$ and $w> -1$ phases, while this is possible with non-trivial GB couplings, even for constant dilaton phase of the standard picture. Within our model, after a sufficient amount of e-folds of expansion, the rolling of both fields $\phi$ and $\sigma$ can be small. In turn, any possible violation of equivalence principle or deviations from the standard general relativity may be small enough to easily satisfy all astrophysical and cosmological constraints.