Eur. Phys. J. C (2026) 86: 96
https://doi.org/10.1140/epjc/s10052-026-15315-w

Regular Article - Theoretical Physics

A new Rényi holographic dark energy model and its cosmological implications

¹ Department of Physics, Sa.C., Islamic Azad university, Sanandaj, Iran
² Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Kurdistan, Iran
³ Department of Physics, Bu-Ali Sina University, P.O. Box 65178, Hamedan, Iran

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Received: 29 November 2025
Accepted: 10 January 2026
Published online: 31 January 2026

Abstract

We develop a generalized holographic dark energy model based on the Rényi entropy, which introduces a logarithmic deformation of the Bekenstein–Hawking entropy and is characterized by a non-extensivity parameter $\alpha$. By adopting the future event horizon as the infrared cutoff, we formulate the New Rényi Holographic Dark Energy (NRHDE) scenario and derive a modified holographic energy density that reduces smoothly to the standard HDE limit for $\alpha \to 0$. Starting from the Rényi entropy formalism, we obtain a closed and self-consistent set of evolution equations for the dark energy density parameter ${\mathrm{\Omega }}_d$, the equation-of-state parameter $w_d$, and the deceleration parameter q. We perform a detailed numerical investigation of the background dynamics over a physically reasonable range of the holographic parameter c and the Rényi deformation parameter $\alpha$, and show that the NRHDE model predicts a late-time phantom regime over an extended region of the $(c,\alpha )$ parameter space, with a smooth approach toward the cosmological-constant boundary $w_d=-1$ as either parameter increases. We further provide a global characterization of the parameter space by means of two-dimensional maps of the present-day equation-of-state parameter and the transition redshift, which clarify the joint impact of $(c,\alpha )$ on the late-time cosmological evolution. Finally, a qualitative comparison between the NRHDE background predictions and observational Hubble data from cosmic chronometers is presented as a consistency check of the model at the background level. The NRHDE framework therefore constitutes a minimal and thermodynamically motivated extension of holographic dark energy, offering a flexible platform for future quantitative tests with late-time expansion data.