ALGEBRAIC INTEGRABILITY OF FRW-SCALAR COSMOLOGIES

Abstract

For dynamical systems of dimension three or more the question of integrability or nonintegrability is extended by the possibility of chaotic behaviour in the general solution. We determine the integrability of isotropic cosmological models in general relativity and string theory with a variety of matter terms, by a performance of the Painleve analysis in an effort to examine whether or not there exists a Laurent expansion of the solution about a movable pole which contains the number of arbitrary constants necessary for a general solution. The question of integrability in the context of cosmological dynamical systems is intimately linked with their asymptotic states for small or large times and is obviously connected with the nature of the singularities present in homogeneous cosmologies. This question cannot be fully addressed via special exact solutions since they are not easily matched to characterize generic features of the models. Qualitative methods, on the other hand, may serve such a purpose and the so-called Painleve analysis is one such approach for testing integrability in an algebraic sense. In this Research Announcement, a start is made of the Painlevanalysis of different cosmologies that arise in general relativity and string theory, in an effort to shed light to the question of whether or not integrability is a generic property characterizing cosmological dynamics (for the first results in this connection see 1 ). 1. The two-fluid FRW model in general relativity is described by the system, u = 1 (b x)cos2cos