Cosmological Analysis of $f(R, Σ, T)$ Gravity with EoS Parameterization

TL;DR

This work develops a cosmological model in $f(R, \Sigma, T)$ gravity with nonlinear matter-geometry coupling, implemented in a spatially flat FRW universe and constrained via a CPL EoS parameterization. By solving the modified Friedmann equations and fitting to cosmic chronometer $H(z)$ data and Pantheon+ SN Ia observations with MCMC (emcee), the authors obtain best-fit values that closely resemble $\Lambda$CDM, with $\omega_0$ near $-1$ and $\omega_a$ consistent with zero, while allowing mild deviations through positive $\eta$ and $b$. The model predicts a negative isotropic pressure, a density evolution consistent with cosmic expansion, and a late-time SEC violation that aligns with acceleration, all while satisfying NEC and DEC. The derived age of the universe, $t_0 \approx 13.79$ Gyr, agrees with Planck 2018 measurements, supporting the viability of $f(R, \Sigma, T)$ gravity as a candidate for explaining late-time acceleration without invoking exotic dark components. Overall, the framework provides a flexible yet consistent alternative to $\Lambda$CDM that remains compatible with current data and offers testable predictions for future surveys.

Abstract

In this paper, we present a comprehensive cosmological analysis within the framework of $f(R, Σ, T)$ gravity, a modified theory that incorporates nonlinear matter-geometry coupling via the inclusion of both the trace of the energy-momentum tensor $T$ and the scalar $Σ= T_{μν}T^{μν}$. We consider a spatially flat Friedmann-Robertson-Walker (FRW) universe and introduce a linear parameterization for the equation of state (EoS) parameter based on the Chevallier-Polarski-Linder (CPL) form, which allows us to explore the dynamical evolution of dark energy without imposing restrictive assumptions. To confront the theoretical model with observations, we utilize the latest Hubble parameter measurements from cosmic chronometers. The model parameters are constrained using Markov Chain Monte Carlo (MCMC) simulations with the \texttt{emcee} package, leading to tight bounds on the parameters. The analysis reveals that the model remains consistent with the $Λ$CDM scenario while allowing mild deviations consistent with observational data. Furthermore, we examine the physical and kinematical features of the model by studying the behavior of the physical parameters. Finally, the calculated age of the universe within this framework is found to be in excellent agreement with Planck 2018 results, highlighting the and viability of $f(R, Σ, T)$ gravity as a candidate for explaining late-time cosmic acceleration.

Figures (7)

• Figure 1: The $1\sigma$ and $2\sigma$ two-dimensional contours confidence areas by using the $31$ CC data sets and Type Ia supernovae obtained from the Pantheon plus (PP) sample in $\eta$-$b$ plane (left panel) and $\omega_{0}$ - $\omega_{a}$ plane (right panel) of the derived model.
• Figure 2: Graphical behavior of pressure versus redshift.
• Figure 3: Graphical behavior of energy density versus redshift.
• Figure 4: Graphical behavior of equation of state parameter versus redshift.
• Figure 5: Graphical behavior of null energy condition versus redshift.