The Cutoff That Was Chosen: Granda–Oliveros Holographic Dark Energy, Censused

Holographic dark energy promises the best kind of explanation: derive the universe's acceleration from a principle — the holographic bound on entropy — instead of fitting it. The Granda–Oliveros construction is the family's most-studied member: an infrared cutoff built from the expansion rate and its derivative, L⁻² = αH² + βḢ, giving a dark-energy density ρ_DE = 3c²M_p²(αH² + βḢ) with two dimensionless parameters. A 2023 analysis by Manoharan took the construction apart and found the load-bearing step: the model's ability to produce late-time acceleration comes "only due to the integration constant that appears by construction" — the value of the dark-energy fraction today is not an output of the model but an input, inserted by hand when the equations are solved, after which the fitted parameters (β = 0.686 ⁺⁰·⁰⁴⁸₋₀·₀₄₄ against current data, with the present equation of state landing at w = −0.988, within 0.3 sigma of a pure cosmological constant) steer the solution onto the ΛCDM track it was advertised to replace. The statistical verdict of the same analysis: the construction is "equally likely as the ΛCDM model, ultimately favouring the latter." This paper censuses the construction step by step — the saturated inequality, the chosen cutoff, the integration constant, the fitted pair — and prices what remains of the holographic promise after each: a two-parameter family that contains ΛCDM as a special case and is preferred by no dataset over it. Grade: ASSUMED, FITTED, AND LANDED ON ΛCDM — CENSUSED. This paper stands outside my work on the vacuum catastrophe; it prices a dark-energy construction, not the vacuum problem, and it neither spends that ledger nor repairs it — the vacuum catastrophe stands not solved in my books regardless of what any dark-energy parametrization does.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23925891
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

The Cutoff That Was Chosen: Granda–Oliveros Holographic Dark Energy, Censused

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

The Cutoff That Was Chosen: Granda–Oliveros Holographic Dark Energy, Censused

William Alexander Aldred
preprint en

Abstract

Holographic dark energy promises the best kind of explanation: derive the universe's acceleration from a principle — the holographic bound on entropy — instead of fitting it. The Granda–Oliveros construction is the family's most-studied member: an infrared cutoff built from the expansion rate and its derivative, L⁻² = αH² + βḢ, giving a dark-energy density ρ_DE = 3c²M_p²(αH² + βḢ) with two dimensionless parameters. A 2023 analysis by Manoharan took the construction apart and found the load-bearing step: the model's ability to produce late-time acceleration comes "only due to the integration constant that appears by construction" — the value of the dark-energy fraction today is not an output of the model but an input, inserted by hand when the equations are solved, after which the fitted parameters (β = 0.686 ⁺⁰·⁰⁴⁸₋₀·₀₄₄ against current data, with the present equation of state landing at w = −0.988, within 0.3 sigma of a pure cosmological constant) steer the solution onto the ΛCDM track it was advertised to replace. The statistical verdict of the same analysis: the construction is "equally likely as the ΛCDM model, ultimately favouring the latter." This paper censuses the construction step by step — the saturated inequality, the chosen cutoff, the integration constant, the fitted pair — and prices what remains of the holographic promise after each: a two-parameter family that contains ΛCDM as a special case and is preferred by no dataset over it. Grade: ASSUMED, FITTED, AND LANDED ON ΛCDM — CENSUSED. This paper stands outside my work on the vacuum catastrophe; it prices a dark-energy construction, not the vacuum problem, and it neither spends that ledger nor repairs it — the vacuum catastrophe stands not solved in my books regardless of what any dark-energy parametrization does.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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