Matter-Only Late-Time Acceleration via Barrow Entropy in Kaniadakis Statistics
The Barrow correction to the horizon entropy changes the total number of microstates associated with the horizon, whereas the Kaniadakis correction provides an alternate statistical description of these microstates different from Boltzmann-Gibbs statistics. In this paper, we consider the Kaniadakis description of the Barrow-corrected horizon entropy analogous to its description of the standard horizon entropy. The modified Friedmann equations were derived for an $(n+1)$-dimensional non-flat universe through two different approaches --- the law of emergence and the first law of thermodynamics. The generalised second law of thermodynamics was investigated, and the density contrast evolution equation was also derived. We take the universe to be composed of only matter and constrain the model parameters through an MCMC analysis using observational Hubble data, Pantheon+ Type Ia supernovae data, baryon acoustic oscillation distances from the DESI DR2 data release, and $fσ_{8}$ measurements from redshift-space distortions. The Kaniadakis parameter $K$ was constrained away from zero, showing a preference for the $K$-deformed statistical approach. Motivated by recent studies, we considered a wider parameter space for the Barrow index, $Δ\in (-1,1]$. In agreement with observational data, we obtained $Δ= -0.335\pm0.031$, motivating a horizon structure different from Barrow's sphereflake configuration. The present value of the Hubble parameter was constrained as $H_{0}=(66.98 \pm 0.71)$ km/s/Mpc, which leans towards the early-universe Planck estimates; however, late-time data alone are insufficient to study the Hubble tension problem. Analysing the evolution of various cosmological parameters, we conclude that the modified Friedmann dynamics of the model produces a viable expansion history and late-time acceleration without invoking a dark energy component.