A comprehensive analysis of Barrow holographic Chaplygin gas model reconstruction and its cosmological consequences

TL;DR

This paper develops a Barrow holographic dark energy framework and reconstructs a variable modified Chaplygin gas (VMCG) as the dark-energy component in a flat FRW universe. By enforcing a BHDE–VMCG correspondence with BHDE density $\rho_{BHDE}=\gamma L^{\Delta-2}$ and $L=1/H$, the authors obtain a reconstructed Hubble rate $H(z)$ and a corresponding $w_{reconstruct}$ that exhibits quintessence behavior near today and tends toward $-1$ at late times. They analyze the dynamics with statefinder $(r,s)$ and $O_m(z)$ diagnostics, finding trajectories that evolve toward the $\Lambda$CDM point and show interpolation between dust and dark-energy dominated phases. Thermodynamic viability is tested via the generalized second law on the apparent horizon with Barrow entropy, yielding a nondecreasing total entropy. Observational constraints from Stern, BAO, CMB, and Union2 SNe Ia confirm consistency of the reconstructed model and bound the free parameters, supporting the viability of BHVMCG as a late-time cosmology candidate.

Abstract

In the current study, we have reconstructed variable modified Chaplygin gas in the Barrow holographic dark energy framework motivated by many recent studies. We have validated the generalized second law of thermodynamics for the reconstructed model. The permissible values of the reconstructed model have been determined by the recent astrophysical and cosmological observational data. The Hubble parameter is presented in terms of the observable parameters and redshift $z$ and other model parameters. From the Stern data set and joint data set of Stern with BAO and CMB observations, the bounds of the model parameters $(B_{0}, Ω_{bhd0})$ are obtained by the $χ^{2}$ minimization procedure. The best-fit value of the distance modulus $μ(z)$ against redshift $z$ is obtained for the reconstructed model and it is consistent with the SNe Ia union2 sample data.

Figures (10)

• Figure 1: Evolution of reconstructed EoS parameter $w_{reconstruct}$ against redshift $z$ and $\Delta$ for the BHVMCG model. The parameters chosen are $A=0.075$, $\alpha=0.004$, $n=0.00001$, $B_{0}=4$, and $\rho_{VMCG0}=0.006$.
• Figure 2: Evolution of reconstructed total EoS parameter $w_{total,reconstruct}$ against redshift $z$ and $\Delta$ for the BHVMCG model. The parameters chosen are $A=0.003$, $\alpha=0.004$, $n=0.001$, $B_{0}=0.9$, $\rho_{VMCG0}=0.006$ and $\gamma=3.3$.
• Figure 3: Evolution of reconstructed deceleration parameter $q_{reconstruct}$ for the BHVMCG model against redshift $z$. The parameters chosen are $A=0.002$, $\alpha=0.004$, $n=0.005$, $\rho_{VMCG0}=0.007$ and $\Delta=0.008$.
• Figure 4: The statefinder pair $(r,s)$ trajectory for the BHVMCG model. The parameters chosen are $A=0.02$, $B_{0} = 0.001$, $\alpha=0.004$, $\rho_{VMCG0}=0.003$, $n=0.005$ and $\Delta=0.001$.
• Figure 5: Evolution of reconstructed $O_{m}(z)$ diagnostic with respect to redshift $z$ for the BHVMCG model. The parameters chosen are $A = 0.002$, $\gamma = 0.02$, $B_{0}=0.02$, $\alpha=0.5$, $\delta =0.002$, $\rho_{VMCG0}=0.4$, $n=0.001$, $h_{0}=73.8$ and $\beta=0.4$.