Scaling cosmologies, geodesic motion and pseudo-susy

Details Scaling cosmologies, geodesic motion and pseudo-susy Scaling cosmologies, geodesic motion and pseudo-susy

2007-04-12

arxiv.org/abs/0704.1653v3

Class.Quant.Grav.24:4679-4690,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, slight change in title, references added, typos corrected. Version accepted for publication in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/24/18/009

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 $n$-torus.

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