Revealing some cosmological aspects of Kaniadakis entropy

TL;DR

This paper analyzes the cosmological consequences of the Kaniadakis entropy within a flat FLRW background, employing the gravity–thermodynamics conjecture. By using the deformed entropy $S_K=(1/K)\sinh(K S_{BH})$, it derives modified Friedmann equations that naturally yield late-time acceleration through entropy corrections, without requiring a separate cosmological constant. A central result is that the deformation parameter $K$ can mimic a cosmological constant, with a correspondence $\Lambda/3 = \pi K/\sqrt{2}$, and the model approaches a de Sitter phase at late times. The work also discusses thermodynamic consistency, possible microscopic interpretations of $K$ (e.g., holography or quantum gravity), and provides a preliminary numerical estimate of $K$ compatible with current data, while noting that full observational fitting is left for future research.

Abstract

Adopting the modifications induced by the truncated version of the Kaniadakis entropy on the Friedmann equations, we explore some relevant aspects of this cosmological scenario at the background level. We analyze the constraint imposed on the parameter $K$ obtained from the accelerated cosmic expansion condition, and we also study the role of such a parameter as a cosmological constant.

Figures (1)

• Figure 1: Validity region for the term $\frac{KS_{\mathrm{BH}}\hbox{shi}\left(KS_{\mathrm{BH}}\right)}{\cosh\left(KS_{\mathrm{BH}}\right)}$ for which $q(t)<0$ with $\omega=0$ (solid line), $\omega=1/3$ (dotted line) and $\omega=1$ (dashed line).