RHDE models in FRW Universe with two IR cut-offs with redshift parametrization

TL;DR

This paper investigates the behavior of R$ackslash$'enyi holographic dark energy in a flat FRW universe with two IR cut-offs, analyzing cosmological parameters and stability, and demonstrating an accelerating universe with quintom-like behavior.

Contribution

It introduces a novel analysis of RHDE with Hubble and GO horizons as IR cut-offs within $f(R,T)$ gravity, including redshift parametrization and stability assessment.

Findings

EoS parameter shows quintom-like behavior for different $\delta$ values.

The universe exhibits accelerated expansion consistent with recent observations.

IR cut-offs significantly influence the universe's dynamic evolution.

Abstract

In this manuscript, we have researched the cosmic expansion phenomenon in flat FRW Universe through the interaction of the recently proposed R$\grave{e}$nyi holographic dark energy (RHDE). For this reason, we assumed Hubble (H) and Granda--Oliveros (GO) horizons as IR cut-off in the framework of $f(R, T)$ gravity. With this choice for IR cut-off, we can obtain some important cosmological quantities such as the equation of state $\omega_{_T}$, energy density $\rho_{_T}$, density parameter $\Omega_{_T}$, and pressure $p_{_T}$, which are the function of the redshift $z$. It is observed that in both IR cut-offs the EoS parameter displays quintom-like behaviour for three different values of $\delta$. Here we plot these parameters versus redshift $z$ and discuss the consistency of the recent findings. Next, we explore the $\omega_{_T}$-$\omega_{_T}^{'}$ plane and the stability analysis of the dark energy model by a perturbation method. Our findings demonstrate that the Universe is an accelerating model of rapid growth that is explained by quintom like behaviour.Hence the feasibility of the RHDE model with Hubble and GO cut-off is supported by our model. The results indicate that the IR cut-offs play a significant role in the understanding of the dynamics of the universe.