Studying the Supernova luminosity distance in Palatini formalism considering the role of causal structure constant

Abstract: The speed of light is a complicated synthesizer quantity with distinctive origins which lead to coincident values in the standard theory. Due to the fact that different aspects of speed of light do not coincide in the local inertial frame for different Palatini modified gravity theories, when deviating from general relativity, one should consider which aspect of speed of light should be taken into account meticulously and unambiguously. The aim of this study is mainly investigating the modification of the SN Ia luminosity distance, for two f(R) and f(RR) extended theories in the local inertial frame in Palatini formalism considering different aspects of the speed of light. Besides the local inertial frame itself should be determined in the Palatini formalism as a frame in which the Einstein Equivalence Principle is valid. SN Ia luminosity distance should be modified considering the variation of the space-time causal structure constant for two well-known extended models in Palatini formalism.