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) 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 behaviour for other potentials of current interest is deduced by comparison.

Print publication: Issue 23 (7 December 2004)
Received 16 June 2004
Published 9 November 2004