G.U. Khapekar, Mohammad Muzammil Mohammad Mukhtar, Syed Mudassir Syed Iqbal
Department of Mathematics, Jagadamba Mahavidyalaya and Research Center, SGB Amravati University, Achalpur City, Maharashtra, India

Abstract. The current study examines the Barrow Holographic Dark Energy model (BHDE) with the Ricci scalar as the IR cut-off in a flat FLRW line element within the framework of a non-linear f(R,L_m) gravity model. We used f(R,L_m) = R/2 + L_mⁿ, where n is a free parameter. Using a Chi-square test and Markov Chain Monte Carlo (MCMC) simulations on Observational Hubble Data (OHD) with 31 points and Pantheon+SHOES data with 1701 points, we find the best match values for model parameters. The best fit ranges for model parameters are as follows: η = 1.3_-0.09^+0.08, H₀ = 65.97_-2.42^+2.48 km/s/Mpc for OHD and η = 1.2_-0.04^+0.04, >i>H₀ = 72.77_-0.26^+0.24 km/s/Mpc for the Pantheon+SHOES dataset. Our analysis produces a value for H₀ that roughly corresponds with the Planck Collaboration's 2018 estimate of H₀ = 67.4 ± 0.5 km/s/Mpc. Then we examined the behavior of Barrow holographic dark energy density, the equation of state (EoS) parameter and the energy conditions. The equation of state parameter ω in our model reveals that the universe is currently in a quintessence phase. The DEC and WEC confirm the model's credibility due to their positive character. However, the violation of SEC suggests the cosmos is undergoing accelerated expansion. Furthermore, we computed the deceleration parameter q, which indicates a change from a previously decelerating phase to the current phase of accelerating expansion, with q₀ = -0.35 (OHD) and q₀ = -0.4 (Pantheon+SHOES), implying that the current model is in an accelerating phase. Furthermore, the quintessential behavior of the proposed model is validated through the calculation of the Om diagnostic parameter, jerk parameter, and statefinder parameters. Finally, our model is consistent with recent observational studies, accounts for the current accelerating phase, and is similar to the quintessence dark energy hypothesis.

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