Holographic dark energy through Kruglov entropy

Abstract

We study a holographic dark energy model built on the new entropy proposed by Kruglov, $S_K=S_{BH}/(1+γS_{BH}^2)$, with the Granda--Oliveros infrared cutoff $L^{-2}=αH^2+β\dot H$ in a flat universe. The Kruglov entropy is smaller than the Bekenstein--Hawking entropy and has a maximum value. We obtain the energy density of the model, the differential equation for the dark energy density parameter, and the expressions for the equation of state parameter, the deceleration parameter and the squared sound speed. At early times the model behaves like the usual Granda--Oliveros holographic dark energy, and the dark energy follows the background with a constant fraction. At late times the Kruglov correction gives a stable de Sitter future when $α>1$, with the final Hubble rate fixed by the entropy parameter. The model gives a matter era followed by a dark energy era, with a transition from deceleration to acceleration near $z\approx0.66$. For larger values of the entropy parameter the equation of state can cross the phantom divide; for the parameters allowed by the data this happens only in the future, if at all. We constrain the model with 31 cosmic chronometer points, Pantheon+ supernovae and DESI DR2 baryon acoustic oscillation data, together with a big bang nucleosynthesis condition, using a Markov chain Monte Carlo analysis. We find $H_0=68.0\pm1.6$ km\,s$^{-1}$\,Mpc$^{-1}$, $α=1.19^{+0.10}_{-0.08}$, $β=0.61^{+0.06}_{-0.05}$ and the 95\% upper limit $\tilde b=b/H_0^4<0.24$ on the dimensionless Kruglov parameter (for a matter-era dark energy fraction below 0.3), which gives $γ<4.9\times10^{-246}$. The present equation of state is $w_{D0}=-0.83\pm0.03$. The model fits the data slightly better than $Λ$CDM ($Δχ^2=-4.5$) and is equally good by the Akaike criterion, while the Bayesian criterion and the Bayesian evidence prefer $Λ$CDM.