On the phenomenology of extended Brans-Dicke Gravity

TL;DR

This paper develops a designer approach to extended Brans-Dicke gravity, deriving analytical expressions for scalar field evolution, effective Newton's constant, and gravitational slip, enabling exploration of parameter dependencies.

Contribution

It introduces a novel analytical method to study extended Brans-Dicke gravity with fixed Hubble parameter, providing explicit formulas for key cosmological quantities.

Findings

Analytical approximations for scalar field as a function of scale factor.

Expressions for effective Newton's constant at background and linear levels.

Dependence of gravitational slip on fundamental parameters.

Abstract

We introduce a designer approach for extended Brans-Dicke gravity that allows us to obtain the evolution of the scalar field by fixing the Hubble parameter to that of a $w$CDM model. We obtain analytical approximations for $\phi$ as a function of the scale factor and use these to build expressions for the effective Newton's constant at the background and at the linear level and the slip between the perturbed Newtonian potentials. By doing so, we are able to explore their dependence on the fundamental parameters of the theory.