Brans-Dicke theory and the emergence of \Lambda CDM model

TL;DR

This paper explores how Brans-Dicke theory with a scalar potential can produce a universe evolution similar to the CDM model, providing constraints based on recent observational data.

Contribution

It demonstrates the conditions under which Brans-Dicke theory yields a de Sitter attractor mimicking CDM and derives observational constraints on the scalar field.

Findings

Existence of a de Sitter attractor in Brans-Dicke phase space.

Conditions on the Brans-Dicke parameter for CDM-like evolution.

Constraints on gravitational coupling variability and scalar field mass from Planck data.

Abstract

The dynamics of the Brans-Dicke theory with a scalar field potential function is investigated. We show that the system with a barotropic matter content can be reduced to an autonomous three-dimensional dynamical system. For an arbitrary potential function we found the values of the Brans-Dicke parameter for which a global attractor in the phase space representing de Sitter state exists. Using linearized solutions in the vicinity of this critical point we show that the evolution of the Universe mimics the $\Lambda$CDM model. From the recent Planck satellite data, we obtain constraints on the variability of the effective gravitational coupling constant as well as the lower limit of the mass of the Brans-Dicke scalar field at the de Sitter state.