String and M-Theory Cosmological Solutions with Ramond Forms

TL;DR

This paper develops a framework for analyzing cosmological solutions in string theory and M-theory with Ramond form fields, providing exact solutions including singularity-free cases and connections to black p-branes.

Contribution

It introduces a general method to find and classify cosmological solutions with multiple form fields in string/M-theory, including Toda theory solutions and singularity-free models.

Findings

Exact solutions with single and multiple form fields are derived.

A subclass of solutions appears to be free of singularities.

Connections between solutions and black p-branes are established.

Abstract

A general framework for studying a large class of cosmological solutions of the low-energy limit of type II string theory and of M-theory, with non-trivial Ramond form fields excited, is presented. The framework is applicable to spacetimes decomposable into a set of flat or, more generally, maximally symmetric spatial subspaces, with multiple non-trivial form fields spanning one or more of the subspaces. It is shown that the corresponding low-energy equations of motion are equivalent to those describing a particle moving in a moduli space consisting of the scale factors of the subspaces together with the dilaton. The choice of which form fields are excited controls the potential term in the particle equations. Two classes of exact solutions are given, those corresponding to exciting only a single form and those with multiple forms excited which correspond to Toda theories. Although typically these solutions begin or end in a curvature singularity, there is a subclass with positive spatial curvature which appears to be singularity free. Elements of this class are directly related to certain black p-brane solutions.