A new Rényi holographic dark energy model and its cosmological implications

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 α α . 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 α → 0 α → 0 . Starting from the Rényi entropy formalism, we obtain a closed and self-consistent set of evolution equations for the dark energy density parameter Ω d Ω d , the equation-of-state parameter wd 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 α α , and show that the NRHDE model predicts a late-time phantom regime over an extended region of the (c,α ) ( c , α ) parameter space, with a smooth approach toward the cosmological-constant boundary wd=-1 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,α ) ( c , α ) 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.