The Brans-Dicke-Rastall theory

TL;DR

This paper introduces a scalar-tensor gravity theory that incorporates Rastall's idea of non-conservation of energy-momentum, analyzing its solutions and cosmological implications.

Contribution

It formulates a new scalar-tensor theory with two parameters, combining scalar-tensor gravity and Rastall's non-conservation principle, and explores its solutions and cosmological behavior.

Findings

Reproduces GR results when the violation parameter is zero.

Provides exact spherically symmetric solutions including Robinson-Bertotti and Schwarzschild.

Shows the theory allows for various cosmological acceleration/deceleration transitions.

Abstract

We formulate a theory combining the principles of a scalar-tensor gravity and Rastall's proposal of a violation of the usual conservation laws. We obtain a scalar-tensor theory with two parameters $\omega$ and $\lambda$, the latter quantifying the violation of the usual conservation laws. The only exact spherically symmetric solution is that of Robinson-Bertotti besides Schwarzschild solution. A PPN analysis reveals that General Relativity results are reproduced when $\lambda = 0$. The cosmological case displays a possibility of deceleration/acceleration or acceleration/deceleration transitions during the matter dominated phase depending on the values of the free parameters.