Symmetric vacuum scalar--tensor cosmology

TL;DR

This paper investigates point symmetries in vacuum scalar-tensor cosmologies, revealing they occur only in Brans-Dicke theory with a cosmological constant and enabling scale factor duality in flat isotropic models.

Contribution

It identifies specific conditions under which point symmetries exist in scalar-tensor cosmologies and demonstrates their use in generating duality transformations.

Findings

Point symmetries occur only in Brans-Dicke theory with a self-interacting dilaton.

The dilaton potential must be a cosmological constant for symmetries to exist.

Symmetries enable the derivation of scale factor duality in flat isotropic models.

Abstract

The existence of point symmetries in the cosmological field equations of generalized vacuum scalar--tensor theories is considered within the context of the spatially homogeneous cosmologies. It is found that such symmetries only occur in the Brans--Dicke theory when the dilaton field self--interacts. Moreover, the interaction potential of the dilaton must take the form of a cosmological constant. For the spatially flat, isotropic model, it is shown how this point symmetry may be employed to generate a discrete scale factor duality in the Brans--Dicke action.