Holographic dark energy from a new two-parameter entropic functional

Abstract

We formulate an extended holographic dark energy scenario based on a recently proposed two-parameter generalized entropic functional. Unlike constructions that phenomenologically impose modified entropy-area relations at the horizon level, the present framework is rooted in a microscopic entropy functional and the corresponding microstate counting. For bounded systems, the entropy acquires a generalized holographic scaling with two independent area contributions, recovering the Bekenstein-Hawking entropy in the appropriate limits. Implementing this entropy within the holographic principle, we derive a generalized dark energy density containing two distinct holographic sectors, naturally embedding standard holographic dark energy and $Λ$CDM as limiting cases. We analyze the cosmological evolution for both Hubble and future event horizon cutoffs and show that the model successfully reproduces the matter-to-dark-energy transition. The two entropic exponents enrich the dynamics, allowing for quintessence-like behavior or phantom regimes, while remaining compatible with the standard thermal history of the Universe.

Figures (3)

• Figure 1: Evolution of the matter and holographic dark energy density parameters as functions of the redshift $z$, assuming the Hubble horizon as the IR cutoff. Upper panel: holographic dark energy with $\delta=1.7$, $\epsilon=1.8$, $\gamma_\delta=1$ and $\gamma_\epsilon$ determined by requiring $\Omega_{DE}(z=0)\equiv\Omega_{DE0}\approx0.7$ at the present epoch (solid curve), compared with the $\Lambda$CDM evolution (dashed curve). Lower panel: same setup with $\delta=2.2$ and $\epsilon=2.3$. Units are chosen such that $M_p^2=1$.
• Figure 2: Evolution of the holographic dark energy equation-of-state parameter $w_{DE}$ as a function of the redshift $z$, assuming the Hubble horizon as the IR cutoff, for $\delta=1.9$, $\epsilon=1.8$ (solid blue curve) and $\delta=2.2$, $\epsilon=2.1$ (dotted green curve). In both cases, we have fixed $\gamma_\delta$ and $\gamma_\epsilon$ as in Fig. \ref{['OmegaFRWs']}. The red dashed curve corresponds to the $\Lambda$CDM prediction. Units are chosen such that $M_p^2=1$.
• Figure 3: Evolution of the holographic dark energy density parameter as a function of the redshift $z$, assuming the future event horizon as the IR cutoff, for $\delta=0.7$ (solid blue curve) and $\delta=1.3$ (dotted green curve). In both cases, we have fixed $\epsilon=2$, $\gamma_\delta=0.05$, and have determined $\gamma_\epsilon$ by requiring $\Omega_{DE}(z=0)\equiv\Omega_{DE0}\approx0.7$ at the present epoch. The red dashed curve corresponds to the standard description of holographic dark energy. Units are chosen such that $M_p^2=1$.