Entropy Bounds and Holographic Dark Energy: Conflicts and Consensus (2501.18144v2)

Abstract: Cohen, Kaplan, and Nelson's influential paper established that the UV-IR cut-offs cannot be arbitrarily chosen but are constrained by the relation $\Lambda^2 L \lesssim M_p$. Here, we revisit the formulation of the CKN entropy bound and compare it with other bounds. The specific characteristics of each bound are shown to depend on the underlying scaling of entropy. Notably, employing a non-extensive scaling with the von Neumann entropy definition leads to a more stringent constraint, $S_{\text{max}} \approx \sqrt{S_{\text{BH}}}$. We also clarify distinctions between the IR cut-offs used in these frameworks. Moving to the causal entropy bound, we demonstrate that it categorises the CKN bound as matter-like, the von Neumann bound as radiation-like, and the Bekenstein bound as black hole-like systems when saturated. Emphasising cosmological implications, we confirm the consistency between the bounds and the first laws of horizon thermodynamics. We then analyse the shortcomings in standard Holographic Dark Energy (HDE) models, highlighting the challenges in constructing HDE using $\Lambda^2 L \lesssim M_p$. Specifically, using the Hubble function in HDE definitions introduces circular logic, causing dark energy to mimic the second dominant component rather than behaving as matter. We further illustrate that the potential for other IR cut-offs, like the future event horizon in an FLRW background or those involving derivatives of the Hubble function, to explain late-time acceleration stems from an integration constant that cannot be trivially set to zero. In brief, the CKN relation doesn't assign an arbitrary cosmological constant; it explains why its value is small.

• The paper distinguishes extensive (CKN) from non-extensive (von Neumann) entropy bounds, revealing how these differences shape holographic dark energy models.
• It employs causal entropy bound analysis to explain cosmic fluid dynamics and stresses the critical role of appropriate IR cut-offs and integration constants.
• The paper critiques the use of the Hubble parameter in HDE formulations, highlighting circular reasoning and fine-tuning challenges in dynamic dark energy models.

Entropy Bounds and Holographic Dark Energy: Conflicts and Consensus

The paper "Entropy Bounds and Holographic Dark Energy: Conflicts and Consensus" by Manosh T. Manoharan provides an analytical exploration of entropy bounds and their implications for holographic dark energy (HDE) models, focusing on their relation to the cosmological constant problem. The paper revisits the formulation of the Cohen-Kaplan-Nelson (CKN) entropy bound and contrasts it with other bounds, highlighting the specific characteristics dependent on underlying entropy scaling assumptions.

Key Findings

1. Entropy Bound Distinctions: The paper examines the CKN entropy bound alongside the Bekenstein and von Neumann bounds. The CKN bound arises from an extensive entropy scaling, leading to a maximum entropy constraint expressed as $S_{\text{max}} \approx S_{\text{BH}}^{3/4}$. In contrast, the von Neumann bound, derived from non-extensive scaling, results in a more stringent constraint, $S_{\text{max}} \approx S_{\text{BH}}^{1/2}$. These distinctions underscore the critical role of entropy definitions in shaping cosmological implications.
2. Causal Entropy Bound (CEB): The paper also explores the causal entropy bound, identifying different scalings for various entropy bounds in a cosmological context. Under CEB, the CKN bound is matter-like, the von Neumann bound is radiation-like, and the Bekenstein bound resembles black holes. This categorization aids in understanding the role of entropy bounds in delineating cosmic fluid dynamics.
3. Holographic Dark Energy Critique: The paper critiques existing HDE models, underscoring challenges in constructing them with $\Lambda^2 L \lesssim M_p$. It emphasizes the pitfalls of employing the Hubble function in HDE definitions, which leads to circular reasoning and results in dark energy mimicking other cosmic components rather than acting as an independent entity with an equation of state distinct from matter.
4. The Role of Integration Constants and IR Cut-offs: The analysis highlights the necessity of incorporating appropriate infrared (IR) cut-offs—such as the future event horizon or derivatives of the Hubble function in an FLRW background—to explain late-time acceleration. The paper points out that such models' success hinges on a consistent choice of integration constants, independent of trivial zero settings.
5. Connection with Cosmic Coincidence and Dark Energy: While the CKN relation explains why the cosmological constant (CC) value is small, the paper discusses how dynamic dark energy models address the cosmic coincidence problem by tracking and evolving the energy density. However, these models face issues concerning fine-tuning and initial condition sensitivity.

Theoretical and Practical Implications

The research offers insightful implications for theoretical approaches to dark energy and cosmological constant issues. It proposes a more comprehensive understanding of entropy bounds and their integration into cosmological frameworks. Practically, it directs future research toward models that account for entropy scaling as an intrinsic feature of dark energy dynamics.

Speculations on Future Developments

The observations made within the paper pave the way for innovative models of cosmology that reconcile entropy bounds with the laws of thermodynamics. Future explorations could explore the interplay between entropy and quantum field theory adjustments, potentially offering breakthroughs in addressing unresolved cosmological tensions and enhancing the theoretical framework of the holographic principle in cosmology.

Overall, the paper establishes a groundwork for advancing our understanding of universe dynamics in relation to dark energy and entropy, calling for further empirical assessment and theoretical innovation in alignment with contemporary cosmological observations.