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Thermodynamics of the most generalized form of Holographic Dark Energy and some particular cases with Corrected Entropies

Sanghati Saha, Ertan Güdekli, Surajit Chattopadhyay

TL;DR

The paper develops a unified entropic holographic dark energy framework based on the four-parameter entropy $\mathcal{S}_g$ to study early- and late-time cosmology within a viscous interacting FRW universe. It reconstructs GHDE, NOHDE, THDE, and BHDE using corresponding IR cut-offs (Nojiri-Odintsov, Tsallis, Barrow) under multiple scale-factor evolutions, and analyzes cosmological parameters, EoS parameters $w$ and $w_{eff}$, and stability via $c_s^2 \ge 0$. The study demonstrates phantom-like behavior in certain regimes, and confirms the generalized second law of thermodynamics (GSLT) across hubs (Hubble, future event, and particle horizons) for Bekenstein, logarithmic, and power-law entropy corrections, with late-time thermal equilibrium in many cases. Overall, the work provides a coherent, thermodynamically consistent unification of diverse entropies within holographic dark energy and offers insights into the interplay between horizon thermodynamics and cosmic acceleration across cosmic epochs.

Abstract

The holographic cut-off in generalized dark energy (HDE) formalism depends on its cut-off. Following this, a four-parameter generalized entropy has recently been developed. It reduces to various known entropies for appropriate parameter limits in the study of Odintsov, S. D., S. DOnofrio, and T. Paul. (2023) Physics of the Dark Universe, 42 pp: 101277. In the current work, we investigate the evolution of the universe in its early phase and late phase within the framework of entropic cosmology, where the entropic energy density functions are reconstructed within the framework of the equivalence of holographic dark energy and four-parameter generalized entropy (Sg). Along with the reconstruction as mentioned earlier scheme, in this study, we demonstrate that an extensive variety of dark energy (DE) models can be considered distinct and particular candidates for the most generalized four-parameter entropic HDE family, each having their cut-off. We examined several entropic dark energy models in this regard, including the generalized holographic dark energy with Nojiri-Odintsov(NO) cut-off, the Barrow entropic HDE (BHDE) with particle horizon as IR cut-off, the Tsallis entropic HDE (THDE) with future event horizon as IR cut-off, all of three cases are particular cases of the most generalized four parameter entropic holographic dark energy. Inspired by S. Nojiri, and S. D. Odintsov (2006) (General Relativity and Gravitation, 38 p: 1285-1304 ) and (S. Nojiri and S. D. Odintsov, 2017, European Physical Journal C, 77, pp.1-8 ); our current work reports a study on cosmological parameters and thermodynamics with entropy-corrections (logarithmic and power-law) to cosmological horizon entropy as well as black hole entropy with a highly generalized viscous coupled holographic dark fluid along its particular cases.

Thermodynamics of the most generalized form of Holographic Dark Energy and some particular cases with Corrected Entropies

TL;DR

The paper develops a unified entropic holographic dark energy framework based on the four-parameter entropy to study early- and late-time cosmology within a viscous interacting FRW universe. It reconstructs GHDE, NOHDE, THDE, and BHDE using corresponding IR cut-offs (Nojiri-Odintsov, Tsallis, Barrow) under multiple scale-factor evolutions, and analyzes cosmological parameters, EoS parameters and , and stability via . The study demonstrates phantom-like behavior in certain regimes, and confirms the generalized second law of thermodynamics (GSLT) across hubs (Hubble, future event, and particle horizons) for Bekenstein, logarithmic, and power-law entropy corrections, with late-time thermal equilibrium in many cases. Overall, the work provides a coherent, thermodynamically consistent unification of diverse entropies within holographic dark energy and offers insights into the interplay between horizon thermodynamics and cosmic acceleration across cosmic epochs.

Abstract

The holographic cut-off in generalized dark energy (HDE) formalism depends on its cut-off. Following this, a four-parameter generalized entropy has recently been developed. It reduces to various known entropies for appropriate parameter limits in the study of Odintsov, S. D., S. DOnofrio, and T. Paul. (2023) Physics of the Dark Universe, 42 pp: 101277. In the current work, we investigate the evolution of the universe in its early phase and late phase within the framework of entropic cosmology, where the entropic energy density functions are reconstructed within the framework of the equivalence of holographic dark energy and four-parameter generalized entropy (Sg). Along with the reconstruction as mentioned earlier scheme, in this study, we demonstrate that an extensive variety of dark energy (DE) models can be considered distinct and particular candidates for the most generalized four-parameter entropic HDE family, each having their cut-off. We examined several entropic dark energy models in this regard, including the generalized holographic dark energy with Nojiri-Odintsov(NO) cut-off, the Barrow entropic HDE (BHDE) with particle horizon as IR cut-off, the Tsallis entropic HDE (THDE) with future event horizon as IR cut-off, all of three cases are particular cases of the most generalized four parameter entropic holographic dark energy. Inspired by S. Nojiri, and S. D. Odintsov (2006) (General Relativity and Gravitation, 38 p: 1285-1304 ) and (S. Nojiri and S. D. Odintsov, 2017, European Physical Journal C, 77, pp.1-8 ); our current work reports a study on cosmological parameters and thermodynamics with entropy-corrections (logarithmic and power-law) to cosmological horizon entropy as well as black hole entropy with a highly generalized viscous coupled holographic dark fluid along its particular cases.
Paper Structure (16 sections, 70 equations, 22 figures)

This paper contains 16 sections, 70 equations, 22 figures.

Table of Contents

  1. Introduction
  2. RECONSTRUCTION SCHEME FOR DIFFERENT FACES OF HOLOGRAPHIC DARK FLUID IN VISCOUS INTERACTING SCENARIO
  3. Cosmological Settings of Four Parameter Entropic Most Generalized Holographic Dark fluid
  4. Cosmological Settings of Generalized Holographic Dark fluid with Nojiri-Odintsov Cut-Off
  5. Cosmological Settings of Tsallis Entropic Dark Fluid
  6. Cosmological Settings of Barrow Entropic Dark Fluid
  7. Generalized Second Law of Thermodynamics with Bekenstein Entropy of Interacting Different Faces of HDE
  8. Generalized Second Law of Thermodynamics at Hubble Horizon
  9. Generalized Second Law of Thermodynamics at Future Event Horizon
  10. Generalized Second Law of Thermodynamics at Particle Horizon
  11. Generalized second law of thermodynamics under corrected entropies
  12. Thermodynamical Analysis for Logarithmic Corrected Entropy
  13. Thermodynamical Analysis for Power-Law Corrected Entropy
  14. Conclusion
  15. Declaration of competing interest
  16. ...and 1 more sections

Figures (22)

  • Figure 1: Evolution of reconstructed viscous interacting 4-parameter entropic GHDE EoS parameter for the range $b~\text{lies in}~(0,1)$ in hybrid-scale factor scenario.
  • Figure 2: Evolution of reconstructed viscous interacting 4-parameter entropic GHDE effective EoS parameter for the range $b~\text{lies in}~(0,1)$ in hybrid-scale factor scenario.
  • Figure 3: Square speed of sound $C_s^2\ge 0$ in late-time for viscous coupled most generalized 4-parameter entropic GHDE in hybrid-scale factor scenario.
  • Figure 4: Evolution of reconstructed viscous interacting NOHDE EoS parameter for the range $b~\text{lies in}~(0,1)$ in logamediate scenario.
  • Figure 5: Evolution of reconstructed viscous interacting NOHDE effective EoS parameter for the range $b~\text{lies in}~(0,1)$ in logamediate scenario.
  • ...and 17 more figures