Solution generating in scalar-tensor theories with a massless scalar field and stiff perfect fluid as a source

TL;DR

This paper introduces a solution-generating method for scalar-tensor theories with a massless scalar or stiff fluid, utilizing symmetry groups in the Einstein frame to produce exact solutions, including regular inhomogeneous cosmologies.

Contribution

It develops a new algorithm based on symmetry groups to generate exact scalar-tensor solutions from Einstein-minimally-coupled-scalar-field solutions, applicable even when symmetries are absent.

Findings

Constructed explicit exact solutions demonstrating the method.

Produced inhomogeneous cosmological solutions with regular curvature invariants.

Outlined a generalization to scalar-tensor-Maxwell gravity.

Abstract

We present a method for generating solutions in some scalar-tensor theories with a minimally coupled massless scalar field or irrotational stiff perfect fluid as a source. The method is based on the group of symmetries of the dilaton-matter sector in the Einstein frame. In the case of Barker's theory the dilaton-matter sector possesses SU(2) group of symmetries. In the case of Brans-Dicke and the theory with "conformal coupling", the dilaton- matter sector has $SL(2,R)$ as a group of symmetries. We describe an explicit algorithm for generating exact scalar-tensor solutions from solutions of Einstein-minimally-coupled-scalar-field equations by employing the nonlinear action of the symmetry group of the dilaton-matter sector. In the general case, when the Einstein frame dilaton-matter sector may not possess nontrivial symmetries we also present a solution generating technique which allows us to construct exact scalar-tensor solutions starting with the solutions of Einstein-minimally-coupled-scalar-field equations. As an illustration of the general techniques, examples of explicit exact solutions are constructed. In particular, we construct inhomogeneous cosmological scalar-tensor solutions whose curvature invariants are everywhere regular in space-time. A generalization of the method for scalar-tensor-Maxwell gravity is outlined.