Non-Critical Strings in Robertson-Walker Space Time

TL;DR

This paper explores a nonlinear sigma model with a Liouville field interpreted as time, deriving background restrictions and analyzing a specific solution in Robertson-Walker spacetime, relevant for string cosmology.

Contribution

It introduces a novel interpretation of the Liouville field as physical time and derives background constraints in a D+1 dimensional sigma model within Robertson-Walker spacetime.

Findings

Restrictions on space-time dimension based on Weyl invariance

Identification of a special solution in Robertson-Walker background

Insights into non-critical string theory in cosmological settings

Abstract

I consider a D+1 dimensional nonlinear $\sigma$ model based on a possible interpretation of the Liouville field as a physical time. The Weyl invariance of this theory gives us restrictions for the background fields and the parameters of the theory, e.g.\ for trivial background one obtains the known regions for the dimension of the space-time ($\leq$1 or $\geq$25). For a Robertson-Walker space time a special solution of these equations is discussed.