Self-similar scalar cosmologies

Abstract

We study several scalar cosmological models under the self-similar approach. We deduce, by stating and proving general theorems, which is the exact form that must follow the scalar field and the potential in the frameworks of a single scalar field and non-interacting (with a perfect fluid) models. The proofs are carried out by two methods: the matter collineation approach and the Lie group method. The results obtained are absolutely general and valid for all Bianchi models and the flat FRW one. In order to study how the “constant” G may vary we propose, in a phenomenological way, how to incorporate a variable G in the framework of scalar models by modifying the Klein-Gordon equation. This approach is more general than the usual one in the context of the FRW symmetries. We deduce the exact form to be followed by each quantity in these new models. Therefore, to study how the “constants” G and Λ may vary, we propose three scenarios where such constants are considered as time functions: modified general relativity with a perfect fluid, the scalar cosmological models (“quintessence”) in the non-interacting case and a scalar-tensor model with a dynamical Λ. As an example, we study the case of Bianchi VI0 geometry.