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June 28, 20260 citationsOpen Access

Variational Backbone and Regime Closures XXI (Dark-Energy Scale): The Holographic Emergence of the Dark-Energy Scale from Partial Observation Why Λ is horizon-set and tiny; why its numerical value is a clock, not a constant

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YYi

Key Points

  • The research aims to address why the dark-energy curvature is extremely small in relation to Planck units and to conceptualize the coincidence problem.
  • Utilized the virtual boundary model from prior work to relate cosmic horizons to dark energy.
  • Employed Jaynes energy placement and Komar bulk dictionary to derive scaling relations.
  • Analysed structural principles such as Internal Invisibility and area law relevant to curvature readout.
  • The smallness of dark energy, Lambda, is proportional to the inverse square of the horizon radius.
  • Bekenstein-Hawking normalization coefficient cancels, supporting the structural integrity of the model.
  • The coincidence problem remains unclaimed, interpreted as the read fraction of the current epoch.

Abstract

This paper addresses the scale side of the cosmological-constant problem within VBRC. The problem has two faces that are often conflated: the scale problem, which asks why the dark-energy curvature is extremely small in Planck units, and the coincidence problem, which asks why the present fractional value of dark energy is near its observed epoch-dependent value. Part XXI treats the first as the derivation target and explicitly leaves the second as a clock/readout question rather than a constant to be derived. The construction reads the cosmic horizon as the Part I virtual boundary. The unread exterior of the finite cosmological protocol is summarized onto a holographic screen with area-counted surface degrees of freedom, and the horizon-screen instance uses the Part XIV first-law temperature. With Jaynes energy placement, the Komar bulk dictionary, the inherited vacuum-tail equation of state, and the compression-saturation gate, the background curvature readout becomes Lambda proportional to the inverse square of the horizon radius. The smallness of Lambda in Planck units is then the square of the horizon-to-Planck length ratio, not the result of inserting a raw zero-point vacuum sum. Three structural checks make the scale result internal to the series. First, the undetermined Bekenstein-Hawking normalization coefficient cancels from the curvature readout, so the scale survives the open Part XIV surface-density normalization. Second, the equipartition and balance inputs are not treated as unrelated postulates: equipartition is read as the Jaynes placement of energy over the counted horizon degrees, while the balance is the horizon-screen form of the Internal Invisibility bound between surface and bulk readability. Third, saturation is licensed only after the imbalance-compression dictionary identifies the holographic imbalance with the Part II compression residual. The resulting dark-energy scale rests on one structural principle, one inference principle, and one holographic form: Internal Invisibility, Jaynes inference, and the area law. The present value of the fractional dark-energy density is not derived here; it is interpreted as the read fraction of the current epoch. Part XXI therefore addresses the smallness of the cosmological-constant scale, while keeping the coincidence problem as an explicit non-claim.

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Cite This Study

Yi (2026) studied this question.

synapsesocial.com/papers/6a40bab961bb0a67205c682ahttps://doi.org/10.5281/zenodo.20920197
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