Distinguishing f(R) Gravity from General Relativity: A Study on Antimatter Separation Mechanisms

In this paper, we demonstrate that the Einstein field equations with a cosmological constant can be expressed in terms of quantum phase transition formulas. This is based on the equivalence principle, which can be formulated using Laurent series as conversion factors. We begin with the fundamental concepts of general relativity and quantum field theory.This paper explores the differences between \( f(R) \) gravity and General Relativity (GR) by examining the behavior of antimatter in high curvature regions. Specifically, we investigate various \( f(R) \) models to determine which can prevent antimatter from annihilating with matter by inducing a repulsive gravitational effect. Through mathematical derivation, Laurent series analysis, we provide evidence that certain \( f(R) \) functions can create conditions for antimatter separation, a phenomenon not observed in GR.