Low energy effective string cosmology

TL;DR

This paper derives general analytic solutions for four-dimensional string cosmology models with a dilaton and antisymmetric tensor field, analyzing how the $H$-field influences the universe's evolution and singularities.

Contribution

It provides the first comprehensive analytic solutions for string cosmology with $H$-field effects in both FRW and Bianchi I models, including long and short wavelength modes.

Findings

Homogeneous $H$-field modifies scale factor and dilaton evolution.

Solutions exhibit singularities with diverging curvature.

H-field radiation leads to a radiation-dominated universe as late-time attractor.

Abstract

We give the general analytic solutions derived from the low energy string effective action for four dimensional Friedmann-Robertson-Walker models with dilaton and antisymmetric tensor field, considering both long and short wavelength modes of the $H$-field. The presence of a homogeneous $H$-field significantly modifies the evolution of the scale factor and dilaton. In particular it places a lower bound on the allowed value of the dilaton. The scale factor also has a lower bound but our solutions remain singular as they all contain regions where the spacetime curvature diverges signalling a breakdown in the validity of the effective action. We extend our results to the simplest Bianchi I metric in higher dimensions with only two scale factors. We again give the general analytic solutions for long and short wavelength modes for the $H$ field restricted to the three dimensional space, which produces an anisotropic expansion. In the case of $H$ field radiation (wavelengths within the Hubble length) we obtain the usual four dimensional radiation dominated FRW model as the unique late time attractor.