Exact Scaling Solutions in Normal and Brans-Dicke Models of Dark Energy

TL;DR

This paper derives exact cosmological solutions in Einstein and Brans-Dicke theories using a linear relationship between the Hubble parameter and scalar field derivative, revealing new scaling quintessence models without assuming specific potential forms.

Contribution

It introduces a method to obtain exact solutions in dark energy models without prior assumptions on the potential or scale factor, expanding understanding of scalar field cosmologies.

Findings

Derived a class of scaling quintessence models with exponential potentials.

Analyzed stability and relevance of these models for cosmic evolution.

Compared Einstein and Brans-Dicke frameworks in dark energy context.

Abstract

A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is explored in order to derive exact cosmological, attractor-like solutions, both in Einstein's theory and in Brans-Dicke gravity with two fluids: a background fluid of ordinary matter, together with a self-interacting scalar field accounting for the dark energy in the universe. A priori assumptions about the functional form of the self-interaction potential or about the scale factor behavior are not necessary. These are obtained as outputs of the assumed relationship between the Hubble parameter and the time derivative of the scalar field. A parametric class of scaling quintessence models given by a self-interaction potential of a peculiar form: a combination of exponentials with dependence on the barotropic index of the background fluid, arises. Both normal quintessence described by a self-interacting scalar field minimally coupled to gravity and Brans-Dicke quintessence given by a non-minimally coupled scalar field are then analyzed and the relevance of these models for the description of the cosmic evolution are discussed in some detail. The stability of these solutions is also briefly commented on.