On 3+1 Dimensional Scalar Field Cosmologies

Abstract

In this communication, we analyze the case of 3+1 dimensional scalar field cosmologies in the presence, as well as in the absence of spatial curvature, in isotropic, as well as in anisotropic settings. Our results extend those of Hawkins and Lidsey [Phys. Rev. D {\bf 66}, 023523 (2002)], by including the non-flat case. The Ermakov-Pinney methodology is developed in a general form, allowing through the converse results presented herein to use it as a tool for constructing new solutions to the original equations. As an example of this type a special blowup solution recently obtained in Christodoulakis {\it et al.} [gr-qc/0302120] is retrieved. Additional solutions of the 3+1 dimensional gravity coupled with the scalar field are also obtained. To illustrate the generality of the approach, we extend it to the anisotropic case of Bianchi types I and V and present some related open problems.