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The possibility of modifications on general relativity is investigated. Wepropose an alternative theory of gravity constructed with the combination ofRastall and Rainbow theories. The hydrostatic equilibrium equations areobtained in order to test the new theory in neutron stars, whose mass-radiusdiagrams are obtained using modern equations of state of nuclear matter derivedfrom relativistic mean field models and compared with the ones computed by theTolman-Oppenheimer-Volkoff equations. We conclude that substantialmodifications are obtained even for very small alterations on the two freeparameters, making the reproduction of astrophysical observations an easy task.

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