Construction of nonsingular cosmological solutions in string theories

TL;DR

This paper constructs nonsingular bouncing cosmological solutions within string theory frameworks, demonstrating conditions under which the universe avoids singularities and smoothly transitions through a bounce.

Contribution

It provides analytical and numerical methods to find nonsingular bouncing solutions in string cosmology, including effects of matter sources, axions, and higher-order corrections.

Findings

Bouncing solutions are found analytically for $\,\, ext{with}\,\, ext{radiation}$ in the dilatonic Brans-Dicke model.

Numerical solutions show matter sources are crucial for nonsingular bounces at $\, ext{with}\, ext{axion}$.

Complete regular bounces with finite dilaton and curvature are possible for $\, e -1$ theories across dimensions.

Abstract

We study nonsingular cosmological scenarios in a general $D$-dimensional string effective action of the dilaton-modulus-axion system in the presence of the matter source. In the standard dilatonic Brans-Dicke parameter ($\omega=-1$) with radiation, we analytically obtain singularity-free bouncing solutions where the universe starts out in a state with a finite curvature and evolves toward the weakly coupled regime. We apply this analytic method to the string-gas cosmology including the massive state in addition to the leading massless state (radiation), with and without the axion. We numerically find bouncing solutions which asymptotically approach an almost radiation-dominant universe with a decreasing curvature irrespective of the presence of the axion, implying that inclusion of the matter source is crucial for the existence of such solutions for $\omega=-1$. In the theories with $\omega \ne -1$, it is possible to obtain complete regular bouncing solutions with a finite dilaton and curvature in both past and future asymptotics for the general dimension, $D$. We also discuss the case where dilatonic higher-order corrections are involved to the tree-level effective action and demonstrate that the presence of axion/modulus fields and the matter source does not significantly affect the dynamics of the dilaton-driven inflation and the subsequent graceful exit.