Exact Conformal Scalar Field Cosmologies ∗

New exact solutions of Einstein’s gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a FriedmannRobertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour S(t) ∼ tp with p > 1, while another class exhibits a late time approach to the S(t) ∼ t behaviour of the coasting models. Bouncing models which avoid an initial singularity are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided. Work supported in part by a grant from DFFCUL-JNICT/CERN (Program STRIDE/FEDER JN.91.02) E-MAIL: [email protected] E-MAIL:[email protected] E-MAIL: [email protected] 0