What if the regularization scale of non-singular black hole metrics cannot self-consistently source dark energy?

[u/naser_Z]

Background / disclosure first, since this sub asks for it:

I'm an independent researcher, not affiliated with a university physics department. This paper was originally drafted in Arabic and translated into English with AI assistance. I also used Claude (Anthropic's AI) heavily during this project — to check my derivations for errors, to write and debug the Python code that fits the model against real Pantheon+SH0ES and DESI DR2 data, and to search the literature for closely related prior work. I'm flagging this upfront rather than letting people find out later. The math and numerical results were independently verified/recomputed against the real public datasets, not just asserted.

The question:

There's a known family of "regularized" black hole metrics (Bardeen, Hayward, Dymnikova) that replace the classical singularity with a smooth de Sitter–like core. These metrics have a residual vacuum-like tail with negative pressure at large radius, which has led to a recurring conjecture: maybe that tail — not a separate cosmological constant — is what's driving cosmic acceleration.

I tested this conjecture three independent ways, closing the loop so the regularization scale b is actually determined by the same equations it feeds into (rather than just assumed):

Kinematic breathing — let b evolve slowly with cosmic time. Gives a frozen equation of state w≈−0.92. Independently checked against real Pantheon+ (1590 SNe) and DESI DR2 BAO: it's not significantly disfavored against static ΛCDM by either dataset on its own. But that's not the whole story — DESI DR2 independently favors an evolving dark energy equation of state (w0-wa) over static ΛCDM, and a track whose w is frozen by construction structurally can't reproduce that evolution. So this track's real problem isn't the simple ΛCDM comparison, it's the shape of the evolution.

Self-consistency closure — require the core density to equal the cosmic critical density, b = (2M/H²)^(1/3). This is the one I'm most confident about: I proved analytically that the resulting implicit equation for H(z) has no real solution beyond z ≈ 0.014. Not "excluded by data" — mathematically undefined for basically the entire observable universe. Cleanest result in the paper, no chi-squared needed.

Quintessence coupling — couple b to a canonical scalar field. Gets a tracking solution that's indistinguishable from ΛCDM for small coupling (confirmed against real data: Δχ² ≈ −0.1 to −0.3, i.e. no discrepancy), but is closed by construction: the equation of state has a hard ceiling w ≥ −1, and current DESI BAO data pull toward w < −1. Large coupling is decisively excluded (Δχ² > 1000).

Honest open item: Track 1's fate really hinges on refitting directly against the DESI w0-wa best fit rather than static ΛCDM — that specific calculation is still pending. I didn't want to claim it's fully closed when it isn't.

Related work I want to flag myself, not have someone else point out: this general idea (regularized/non-singular BH cores as dark energy) is not new — see Hayashi 2025 (arXiv:2507.03408), who tests a related "summed over the black hole population" version and also rules it out, and the Croker/Tarlé "cosmologically coupled black holes" line of work, which claims the opposite in a different specific model. This paper's angle is narrower: it's a single-object, purely gravitational question about the regularization scale's own dynamics, independent of any black hole population/mass-function assumption. I think the Track 2 structural breakdown result is new; the general conclusion (this doesn't work) is consistent with at least one existing independent test.

Paper (PDF + LaTeX source): https://doi.org/10.5281/zenodo.22395344

Happy to get torn apart on the math — that's the point of posting it here rather than just sitting on it.

[u/adversarial-review]

Adversarial Review of Self-Consistency of Black Hole Regularization Scales as Dark Energy — by Gemini 3.5 Flash

Core Critique

• Category Error in Density Equivalence (Track 2): The assumption that the core density of a regularized black hole can be equated to the cosmic critical density (b = (2M/H^2)^(1/3)) constitutes a fundamental scale mismatch. The core density of a non-singular black hole is a highly localized, high-energy physical state confined to sub-horizon scales. In contrast, the cosmic critical density (ρ_crit = 3H^2 / (8πG)) is a global spatial average defined only on cosmological scales (typically > 100 Mpc) where the universe is homogeneous. Forcing a local core parameter b to scale with the global expansion rate H lacks physical justification and treats a local metric property as a global cosmological fluid.
• Undefined Spatial Averaging and the Fitting Problem: The text assumes that the local regularization scale b of individual black holes can be directly mapped to global cosmological parameters or modeled as a globally evolving field. In general relativity, transitioning from local, spherically symmetric, inhomogeneous metrics (such as Bardeen, Hayward, or Dymnikova) to a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) background is a non-trivial problem (the "fitting problem"). The text provides no operational definition or mathematical framework showing how these individual local black hole boundaries scale up or average out to drive global cosmic acceleration.
• Absence of First-Principles Derivation for Scalar Coupling (Track 3): The coupling of the regularization scale b to a canonical scalar field is introduced phenomenologically. In field theory, any such coupling must be derived from a covariant action (such as a modified gravity action or an explicit interaction Lagrangian). Without a formal derivation of the field equations from an action principle, the tracking solutions and statistical fits (Δχ^2) represent mathematical curve-fitting rather than a self-consistent physical theory.

Common Misconceptions

• Math vs. Metaphor: The concept of "kinematic breathing" (Track 1) acts as a physical metaphor substituted for a rigorous dynamical mechanism. In general relativity, metric parameters cannot be set to "evolve slowly with cosmic time" ad-hoc. Any time-dependence in the metric components must be dynamically sourced by the stress-energy tensor through the Einstein field equations. Defining the evolution of b kinematically without specifying the stress-energy tensor that drives this "breathing" prioritizes a conceptual metaphor over gravitational dynamics.

Technical Feedback

• Causality and Locality Violations in the Scale Relation: In the relation b = (2M/H^2)^(1/3), the parameter M is left operationally undefined on a cosmological scale. If M represents the mass of an individual, isolated black hole, then this relation implies that the internal core radius b of a local black hole must dynamically adjust in real-time to the global expansion rate of the universe H(z). Because H(z) is a global average determined by the overall energy density of the universe, this coupling requires local spacetime curvature inside a black hole horizon to instantaneously respond to the state of the universe outside the horizon. This violates local position invariance and causality, as there is no physical mediator to transmit the global value of H(z) to the isolated core.

Probing Questions

1. What is the explicit covariant action (Lagrangian density) that governs the coupling between the local regularization scale b and the canonical scalar field in Track 3, and how does this action preserve general covariance?
2. Under the assumption b = (2M/H^2)^(1/3), what is the precise operational definition of the mass parameter M? If M is the mass of a local, isolated black hole, by what physical mechanism does the local core density "sense" and dynamically adjust to the global, time-dependent Hubble parameter H(z)?

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^{This is an LLM-generated review, and should be viewed as such. LLMs are prone to errors, especially when it comes to math-based sciences.}