Scaling solutions and geodesics in moduli space
arXiv:hep-th/0604046 · doi:10.1088/0264-9381/23/14/004
Abstract
In this paper we consider cosmological scaling solutions in general relativity coupled to scalar fields with a non-trivial moduli space metric. We discover that the scaling property of the cosmology is synonymous with the scalar fields tracing out a particular class of geodesics in moduli space - those which are constructed as integral curves of the gradient of the log of the potential. Given a generic scalar potential we explicitly construct a moduli metric that allows scaling solutions, and we show the converse - how one can construct a potential that allows scaling once the moduli metric is known.
10 pages, 3 figures