paper

Cosmology as Geodesic Motion

arXiv:hep-th/0404241 · doi:10.1088/0264-9381/21/23/006

Abstract

For gravity coupled to N scalar fields with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N+1)-dimensional `augmented' target space of Lorentzian signature (1,N), timelike if V>0, null if V=0 and spacelike if V<0. Accelerating cosmologies correspond to timelike geodesics that lie within an `acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are shown to evolve as projections of geodesic motion in a space of dimension (N+2), of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. This formalism is illustrated by cosmological solutions of models with an exponential potential, which are comprehensively analysed; the late-time behviour for other potentials of current interest is deduced by comparison.

26 pages, 2 figures, journal version with additional references

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