# Combined Rastall and Rainbow theories of gravity with applications to neutron stars

## TL;DR

This paper introduces a novel gravity theory combining Rastall and Rainbow models, analyzing its effects on neutron star structure and showing it can easily match astrophysical observations with small parameter adjustments.

## Contribution

It develops a new gravity framework merging Rastall and Rainbow theories and applies it to neutron star modeling, expanding the scope of modified gravity theories.

## Key findings

- Modified gravity significantly affects neutron star mass-radius relations.
- Small parameter changes produce substantial deviations from general relativity.
- The theory can replicate observed neutron star properties with minimal parameter tuning.

## Abstract

The possibility of modifications on general relativity is investigated. We propose an alternative theory of gravity constructed with the combination of Rastall and Rainbow theories. The hydrostatic equilibrium equations are obtained in order to test the new theory in neutron stars, whose mass-radius diagrams are obtained using modern equations of state of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff equations. We conclude that substantial modifications are obtained even for very small alterations on the two free parameters, making the reproduction of astrophysical observations an easy task.