Brans-Dicke unimodular gravity

TL;DR

This paper introduces a unimodular version of Brans-Dicke gravity with traceless field equations, revealing new stability properties of scalar modes while preserving tensor mode behavior.

Contribution

It formulates a constrained Lagrangian version of unimodular Brans-Dicke gravity, analyzing its solutions and stability, which differs from standard Brans-Dicke theory.

Findings

Vacuum solutions include a cosmological constant term.

Scalar modes exhibit both stable and unstable configurations.

Tensor modes remain unchanged from traditional Brans-Dicke theory.

Abstract

We propose a unimodular version of the Brans-Dicke theory designed with a constrained Lagrangian formulation. The resulting field equations are traceless. The vacuum solutions in the cosmological background reproduce the corresponding solutions of the usual Brans-Dicke theory but with a cosmological constant term. A perturbative analysis of the scalar modes is performed and stable and unstable configurations appear in contrast with the Brans-Dicke case for which only stable configurations occur. On the other hand, tensorial modes in this theory remains the same as in the traditional Brans-Dicke theory.