Self-similar cosmological solutions with a non-minimally coupled scalar field

TL;DR

This paper finds self-similar cosmological solutions involving a scalar field with non-minimal coupling, revealing conditions for accelerated expansion and scalar field behavior similar to a cosmological constant.

Contribution

It introduces a comprehensive analysis of fixed points in scalar-tensor cosmologies with arbitrary potentials, including a novel scaling solution and insights into late-time acceleration.

Findings

Scalar field can mimic a cosmological constant in strong coupling.

Decoupling of radiation from scalar field is automatic.

Energy transfer can induce late-time acceleration.

Abstract

We present self-similar cosmological solutions for a barotropic fluid plus scalar field with Brans-Dicke-type coupling to the spacetime curvature and an arbitrary power-law potential energy. We identify all the fixed points in the autonomous phase-plane, including a scaling solution where the fluid density scales with the scalar field's kinetic and potential energy. This is related by a conformal transformation to a scaling solution for a scalar field with exponential potential minimally coupled to the spacetime curvature, but non-minimally coupled to the barotropic fluid. Radiation is automatically decoupled from the scalar field, but energy transfer between the field and non-relativistic dark matter can lead to a change to an accelerated expansion at late times in the Einstein frame. The scalar field density can mimic a cosmological constant even for steep potentials in the strong coupling limit.