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arxiv: 2606.23522 · v1 · pith:LP6XZP3Xnew · submitted 2026-06-22 · ✦ hep-th · gr-qc

Microscopic entropy of de Sitter spacetime and entropic solution to the old cosmological constant problem

Mariano Cadoni , Lorenzo Herres , Lorenzo Orlando , Mirko Pitzalis This is my paper

Pith reviewed 2026-06-26 07:19 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords de Sitter spacetimecosmological constantBekenstein-Hawking entropyrenormalization group flowWeyl symmetryscale symmetryemergent gravityholography
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The pith

The dimensionless ratio of de Sitter to Planck scales equals the Bekenstein-Hawking entropy of de Sitter space, and its monotonic renormalization-group flow sets the cosmological constant to the observed value.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a dimensionless coupling α arising from Weyl symmetry breaking in conformal gravity and residual scale symmetry in Einstein gravity equals the Bekenstein-Hawking entropy of de Sitter spacetime. It gives α a microscopic reading as the number of degrees of freedom tied to the de Sitter horizon by combining functional renormalization group ideas, holography, and emergent gravity. The renormalization group flow of α(k) tracks how these degrees of freedom vary with scale. Requiring the flow to increase monotonically toward the infrared produces a cosmological constant whose magnitude matches observations. The result follows directly from the very large number of horizon degrees of freedom in de Sitter space.

Core claim

α is the Bekenstein-Hawking entropy of de Sitter spacetime and counts the microscopic degrees of freedom on its horizon. The renormalization group flow of α(k) encodes the scale dependence of these degrees of freedom. Requiring monotonic increase of the flow toward the infrared fixes the cosmological constant at the observed order as a direct consequence of the enormous number of degrees of freedom in our de Sitter universe.

What carries the argument

The dimensionless coupling α, identified as the Bekenstein-Hawking entropy of de Sitter spacetime and as a count of horizon degrees of freedom, with its renormalization group flow required to increase monotonically in the infrared.

If this is right

  • The observed cosmological constant follows directly from the monotonic infrared flow of the entropy parameter α.
  • The smallness of the cosmological constant is a consequence of the extraordinarily large number of microscopic degrees of freedom on the de Sitter horizon.
  • Weyl symmetry breaking together with residual scale symmetry determines the scale dependence of horizon entropy.
  • The entropic counting of degrees of freedom supplies a first-principles account of the old cosmological constant problem.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The monotonicity requirement may impose new constraints on quantum gravity constructions that include de Sitter horizons.
  • The same entropic flow logic could be examined in other holographic or emergent-gravity settings beyond pure de Sitter space.
  • Consistency checks could compare the result obtained from different renormalization-group schemes or from direct horizon entropy calculations.

Load-bearing premise

The renormalization group flow of α(k) must increase monotonically toward the infrared.

What would settle it

An explicit computation of the beta function for α that shows the flow decreases or becomes non-monotonic in the infrared would falsify the mechanism for obtaining the observed cosmological constant.

read the original abstract

We study the role of Weyl symmetry breaking in conformal gravity and the residual scale symmetry of Einstein gravity. The corresponding action is characterized by a dimensionless coupling $\alpha$, determined by the ratio between the de Sitter and Planck scales. We show that this quantity admits a natural interpretation as the Bekenstein-Hawking entropy of de Sitter spacetime. Combining ideas from the functional renormalization group, holography, and emergent gravity, we propose a microscopic interpretation of $\alpha$ as a measure of the degrees of freedom associated with the de Sitter horizon. In this framework, the renormalization group flow of $\alpha(k)$ encodes the scale dependence of these microscopic degrees of freedom. Requiring this flow to be monotonically increasing toward the infrared leads to a cosmological constant of the same order as the observed one, suggesting an entropic solution to the old cosmological constant problem. This remarkably small value can therefore be understood as a direct consequence of the extraordinarily large number of degrees of freedom in our de Sitter universe.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper studies Weyl symmetry breaking in conformal gravity and the residual scale symmetry in Einstein gravity, identifying a dimensionless coupling α as the ratio of de Sitter to Planck scales. It interprets α as the Bekenstein-Hawking entropy of de Sitter spacetime and, via functional RG, holography and emergent gravity, as a count of microscopic horizon degrees of freedom. The RG flow α(k) is then required to increase monotonically toward the infrared, which is claimed to fix the cosmological constant to the observed magnitude and thereby solve the old CC problem.

Significance. If an independent derivation of the monotonicity condition were supplied from the functional RG plus holographic setup, the work would offer a novel microscopic, entropic account of the small observed CC tied to the large number of de Sitter degrees of freedom. At present the result rests on an imposed rather than derived condition, limiting its significance.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'requiring this flow to be monotonically increasing toward the infrared leads to a cosmological constant of the same order as the observed one' is not accompanied by a derivation of the beta function for α(k) or a demonstration that monotonicity follows from the functional RG, holography or emergent-gravity ingredients; the condition is introduced to recover the target value.
  2. The identification of α with both the de Sitter entropy and the microscopic dof count is used to motivate the flow equation, yet no explicit beta function or renormalization-group equation is supplied that would independently enforce dα/dk > 0 (or equivalent) without additional input.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. The feedback points to the need for greater clarity on the status of the monotonicity condition in our proposal. Below we address the major comments point by point.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'requiring this flow to be monotonically increasing toward the infrared leads to a cosmological constant of the same order as the observed one' is not accompanied by a derivation of the beta function for α(k) or a demonstration that monotonicity follows from the functional RG, holography or emergent-gravity ingredients; the condition is introduced to recover the target value.

    Authors: We agree that the monotonicity condition is introduced as a physical requirement rather than derived from the functional RG equations in the present work. The paper combines ideas from functional RG, holography, and emergent gravity to motivate the interpretation of α as the microscopic entropy, but does not compute an explicit beta function β_α(k) that would independently imply dα/dk > 0. Instead, the monotonic increase toward the IR is posited based on the expectation that the number of horizon degrees of freedom grows as the scale decreases, consistent with the large observed entropy. This leads to the small CC. We will revise the abstract and introduction to make this clearer and discuss the physical motivation in more detail. revision: partial

  2. Referee: The identification of α with both the de Sitter entropy and the microscopic dof count is used to motivate the flow equation, yet no explicit beta function or renormalization-group equation is supplied that would independently enforce dα/dk > 0 (or equivalent) without additional input.

    Authors: The identification of α with the Bekenstein-Hawking entropy and the dof count is used to provide physical motivation for considering the RG flow of α(k). However, as noted, no explicit RG equation is derived that enforces the monotonicity without the additional assumption. The manuscript proposes this as a way to solve the CC problem via the entropic interpretation, but the referee is correct that the monotonicity is an input. In the revision, we will make this distinction clearer and discuss potential ways in which future work could derive such a beta function from the underlying holographic or emergent gravity setup. revision: partial

standing simulated objections not resolved
  • An explicit derivation of the beta function for α(k) from the functional RG, holography, or emergent gravity that would enforce the monotonicity condition without additional physical input.

Circularity Check

1 steps flagged

Monotonicity of RG flow for α(k) imposed to recover observed CC value rather than derived

specific steps
  1. fitted input called prediction [abstract]
    "Requiring this flow to be monotonically increasing toward the infrared leads to a cosmological constant of the same order as the observed one, suggesting an entropic solution to the old cosmological constant problem."

    The observed small CC is recovered precisely by imposing monotonic increase of α(k) in the IR; the paper presents this requirement as the mechanism that solves the problem, but supplies no derivation that the beta function or holographic dof counting forces monotonicity rather than permitting other behaviors consistent with the microscopic counting.

full rationale

The paper identifies α with de Sitter entropy and proposes its RG flow encodes microscopic dof. The central result—that the flow yields a CC of observed magnitude—rests on the explicit requirement that the flow be monotonically increasing toward the IR. This condition is stated in the abstract as the step that produces the small value, with no independent derivation from the functional RG equations, holography, or dof counting showing why dα/dk > 0 must hold. The outcome is therefore selected by the monotonicity assumption chosen to match the target, reducing the entropic 'solution' to a consistency condition rather than an output of the framework.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on the interpretation of α as microscopic degrees of freedom and on the externally imposed monotonicity of its RG flow; both are introduced without independent derivation in the abstract.

free parameters (1)
  • α
    Dimensionless coupling fixed by de Sitter-to-Planck scale ratio and interpreted as entropy; its infrared value is fixed by the monotonic-flow requirement.
axioms (2)
  • domain assumption Weyl symmetry breaking in conformal gravity produces a residual scale symmetry whose coupling α is the Bekenstein-Hawking entropy of de Sitter space.
    Stated as the starting point of the analysis.
  • ad hoc to paper The RG flow α(k) is monotonically increasing toward the infrared.
    This condition is required to obtain the observed cosmological constant.

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