A study on causality in $f(R,\phi,X)$ theory

TL;DR

This paper investigates causality issues in the $f(R,\, ext{ extphi},X)$ gravity model within G"odel-type universes, analyzing conditions for causal and non-causal solutions and how matter content influences causality violation.

Contribution

It provides a detailed analysis of causality violation in $f(R, extphi,X)$ gravity, including critical radius calculations and matter dependence, which is a novel exploration in modified gravity theories.

Findings

Causal and non-causal solutions coexist in the model.

A critical radius for non-causal solutions is derived.

Causality violation depends on matter content.

Abstract

The $k$-essence modified $f(R)$ gravity model, i.e., $f(R,\phi,X)$ theory is studied. The question of violation of causality, in the framework of G\"{o}del-type universes, is investigated in this gravitational model. Causal and non-causal solutions are allowed. A critical radius for non-causal solution is calculated. It is shown that the violation of causality depends on the content of matter.