Anisotropic homogeneous string cosmology with two-loop corrections

TL;DR

This paper investigates anisotropic homogeneous string cosmologies by solving two-loop corrected equations for all Bianchi types, providing explicit solutions for metric, dilaton, and B-field at first-order $eta$-function corrections.

Contribution

It offers the first comprehensive solutions of two-loop corrected string equations for all Bianchi models in two different effective action schemes.

Findings

Explicit solutions for metric, dilaton, and B-field at $eta$-function two-loop order.

Comparison of $R^2$ and Gauss-Bonnet schemes in string cosmology.

Extension of string cosmology models to include two-loop quantum corrections.

Abstract

The two-loop (order $\alpha'$) $\beta$-function equations, which are equivalent to the equations of motion of $\alpha'$-corrected string effective action, are considered for anisotropic homogeneous space-times. These equations are solved for all Bianchi-type models in two schemes of effective action, namely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then the metric, dilaton and $B$-field are found at $\alpha'$ perturbative corrections.