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Infrared Corrections and Horizon Phase Transitions in Kaniadakis-Based Holographic Dark Energy

Manuel Gonzalez-Espinoza, Samuel Lepe, Joel F. Saavedra, Francisco Tello-Ortiz

Abstract

We study the cosmological and thermodynamic implications of holographic dark energy derived from the Kaniadakis deformation of the Bekenstein-Hawking entropy. Within a spatially flat FLRW background, the generalized entropy leads to an effective dark energy density containing an infrared correction proportional to $H^{-2}$, modifying the dynamics of the apparent horizon. Using the Hayward Kodama formalism, we obtain a geometric equation of state and perform a criticality analysis, revealing a Van der Waals type structure with an inverted first order phase transition and a non physical swallowtail behavior in the Gibbs free energy, indicative of unstable thermodynamic branches. We further examine a dynamical extension including a $\dot{H}$ contribution and show that the unconventional critical behavior persists. The phenomenological viability of the model is tested through a joint statistical analysis with cosmic chronometers, PantheonPlus Type Ia supernovae, and DESI baryon acoustic oscillation data. These results establish Kaniadakis holographic cosmology as a consistent framework linking generalized entropy, gravitational thermodynamics, and observationally viable dark energy dynamics.

Infrared Corrections and Horizon Phase Transitions in Kaniadakis-Based Holographic Dark Energy

Abstract

We study the cosmological and thermodynamic implications of holographic dark energy derived from the Kaniadakis deformation of the Bekenstein-Hawking entropy. Within a spatially flat FLRW background, the generalized entropy leads to an effective dark energy density containing an infrared correction proportional to , modifying the dynamics of the apparent horizon. Using the Hayward Kodama formalism, we obtain a geometric equation of state and perform a criticality analysis, revealing a Van der Waals type structure with an inverted first order phase transition and a non physical swallowtail behavior in the Gibbs free energy, indicative of unstable thermodynamic branches. We further examine a dynamical extension including a contribution and show that the unconventional critical behavior persists. The phenomenological viability of the model is tested through a joint statistical analysis with cosmic chronometers, PantheonPlus Type Ia supernovae, and DESI baryon acoustic oscillation data. These results establish Kaniadakis holographic cosmology as a consistent framework linking generalized entropy, gravitational thermodynamics, and observationally viable dark energy dynamics.
Paper Structure (16 sections, 99 equations, 7 figures, 3 tables)

This paper contains 16 sections, 99 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Kaniadakis entropy and its holographic formulation
  3. The apparent horizon dynamics
  4. Modified holographic dark energy model and the equation of state
  5. Phase transitions and criticality
  6. Classical stability
  7. Modified Friedmann dynamics and observational constraints
  8. Statistical analysis: $\chi^2$ estimators
  9. Model 1
  10. Model 2
  11. Concluding remarks
  12. Cosmological dynamics with generalized holographic dark energy
  13. Deceleration parameter.
  14. Including $\dot{H}$ corrections.
  15. Effective Dark-Energy Equation of State and Regimes
  16. ...and 1 more sections

Figures (7)

  • Figure 1: The trend of the pressure (\ref{['eos1']}) versus the volume for the model \ref{['eq7']}. The system presents an inverted first order phase transition above the critical temperature. This plot considers $\{c,K\}=\{0.2;0.02\}$.
  • Figure 2: Left panel: The Gibbs free energy against the pressure for the model \ref{['eq45']}. For those values below the critical temperature (red line), the Gibbs function is smooth, while increasing the temperature and crossing the critical one (blue line), appear a non-physical swallowtail shape accounting for a non-conventional first order phase transition. Right panel: A zoom of the swallowtail. It should be taking into account that the curve traversed from small to huge volumes. As the pressure increases with volume, the Gibbs free energy never reaches a minimum value as desired for thermodynamic stability.
  • Figure 3: The trend of the pressure (\ref{['eos2']}) versus the volume for the model \ref{['eq45']}. The system presents an inverted first order phase transition above the critical temperature. This plot considers $\{c;K;\beta\}=\{0.6;0.02;0.015\}$.
  • Figure 4: The Gibbs free energy against the pressure for the model \ref{['eq7']}. For those values below the critical temperature (red line), the Gibbs function is smooth, while increasing the temperature and crossing the critical one (blue line), appear a non-physical swallowtail shape accounting for a non-conventional first order phase transition.
  • Figure 5: Triangle plot showing the joint constraints from CC + PantheonPlus + DESI for three fixed values of the parameter $c^2$, for model 1, Eq. \ref{['eq_model1']}. While the inferred value of the present-day matter density $\Omega_{m0}$ shifts systematically as $c$ varies, the posterior distributions of the Hubble constant $H_0$ and the supernova absolute magnitude $M$ remain unchanged. This behavior reflects the exact degeneracy between $\Omega_{m0}$ and $c$ at the background level, indicating that late-time expansion data are insensitive to $c$.
  • ...and 2 more figures