Dark Energy Phenomenology in a $f(R,\Sigma,T)$ Gravity Framework: $O_m(z)$ Parameterization Approach

TL;DR

This paper explores $f(R, ext{sum},T)$ gravity to model dark energy phenomenology, reconstructing the Hubble parameter via $O_m(z)$ to analyze cosmic acceleration and energy conditions.

Contribution

It introduces a model-independent $O_m(z)$ parameterization within $f(R, ext{sum},T)$ gravity, providing a dynamic dark energy model consistent with observations.

Findings

The EoS parameter remains in the quintessence regime, approaching -1 in the future.

The model reproduces the transition from cosmic deceleration to acceleration.

Classical instability is indicated by the analysis of the squared sound speed.

Abstract

This study investigates the cosmological implications of $f(R,\Sigma,T)$ gravity by reconstructing the Hubble parameter from a logarithmic parameterization of the $O_m(z)$ diagnostic. Our approach offers a model-independent way to probe the nature of dark energy and differentiate it from a cosmological constant. We derive the field equations for $f(R,\Sigma,T) = R + \Sigma + 2\pi\eta T$ within the homogeneous, isotropic, and spatially flat Friedmann-Robertson-Walker (FRW) metric. A comprehensive analysis of key physical parameters, including the equation of state (EoS) parameter $\omega(z)$, the $(\omega-\omega')$-plane, the squared sound speed $\vartheta^2$, and various energy conditions (Null, Dominant, Strong), is presented. Our findings reveal a dynamic EoS parameter that consistently remains within the quintessence regime ($-1 < \omega < -1/3$), approaching $\omega = -1$ in the far future, thereby avoiding phantom behavior and maintaining the weak energy condition. The model successfully reproduces the cosmic transition from deceleration to acceleration, as indicated by the deceleration parameter $q(z)$ crossing zero. While the model aligns well with observational data for cosmic expansion, the analysis of $\vartheta^2$ indicates classical instability, a point requiring further theoretical refinement. Overall, this work demonstrates the viability of $f(R,\Sigma,T)$ gravity as a framework capable of describing the universe's accelerated expansion, consistent with current cosmological observations, while offering a dynamic alternative to the $\Lambda$CDM model.