Scaling cosmologies, geodesic motion and pseudo-susy
Abstract
One-parameter solutions in supergravity carried by scalars and a metric trace out curves on the scalar manifold. In ungauged supergravity these curves describe a geodesic motion. It is known that a geodesic motion sometimes occurs in the presence of a scalar potential and for time-dependent solutions this can happen for scaling cosmologies. This note contains a further study of such solutions in the context of pseudo-supersymmetry for multi-field systems whose first-order equations we derive using a Bogomol'nyi-like method. In particular we show that scaling solutions that are pseudo-BPS must describe geodesic curves. Furthermore, we clarify how to solve the geodesic equations of motion when the scalar manifold is a maximally non-compact coset such as occurs in maximal supergravity. This relies upon a parametrization of the coset in the Borel gauge. We then illustrate this with the cosmological solutions of higher-dimensional gravity compactified on a -torus.
Cite
@article{arxiv.0704.1653,
title = {Scaling cosmologies, geodesic motion and pseudo-susy},
author = {Wissam Chemissany and André ploegh and Thomas Van Riet},
journal= {arXiv preprint arXiv:0704.1653},
year = {2008}
}
Comments
14 pages, slight change in title, references added, typos corrected. Version accepted for publication in Class. Quantum Grav