Note on the Evolution of the Gravitational Potential in Rastall Scalar Field Theories

TL;DR

This paper studies how the gravitational potential evolves in Rastall scalar field theories, highlighting the conditions under which perturbation theory aligns with General Relativity and exploring multi-component models.

Contribution

It demonstrates that consistent perturbation theory in Rastall scalar field theories is only possible for the GR limit unless additional fluid components are included.

Findings

Perturbation theory is consistent only at γ=1 in single-component models.

Adding a second fluid component extends the range of γ values for which perturbation theory is valid.

The study clarifies the conditions for gravitational potential evolution in Rastall theories.

Abstract

We investigate the evolution of the gravitational potential in Rastall scalar field theories. In a single component model a consistent perturbation theory, formulated in the newtonian gauge, is possible only for $\gamma = 1$, which is the General Relativity limit. On the other hand, the addition of another canonical fluid component allows also to consider the case $\gamma \neq 1$.