String and M-Theory Cosmological Solutions with Ramond Forms

TL;DR

This work develops a general framework for cosmological solutions in the low-energy limits of type II string theory and M-theory with Ramond-Ramond fields, recasting the dynamics as motion on a moduli space spanned by the scale factors and the dilaton. By classifying form-field contributions into elementary, solitonic, and curvature-induced terms, the authors derive an effective potential that is a sum of exponentials in the moduli coordinates and show exact solutions when this potential reduces to a single term or forms a Toda model. The results reveal how Ramond fields interpolate between Kaluza–Klein backgrounds, produce rich expansion/contraction patterns across multiple subspaces, and, in curved cases, can yield singularity-free or horizon-like cosmologies with connections to black $p$-branes. The work also highlights a deep correspondence between cosmological solutions and spacelike $p$-branes, and discusses explicit examples (e.g., SU(2), SU(3) Toda models) and a Behrndt–Förste-type curved-space solution that illustrates potential singularity resolution. Overall, the framework provides a solvable, unifying approach to string cosmology with RR fields and links to brane physics.

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.