Relocated, Not Retired: The Unimodular Integration Constant, Priced

This paper prices one of the cleanest moves ever made on the cosmological constant problem, and prices it without discount in either direction. In 1989 Henneaux and Teitelboim showed that in unimodular gravity the cosmological constant enters as an integration constant rather than as a coupling in the action: vacuum fluctuations decouple from the gravitational Λ at the classical level, and the question changes from why a coupling is small to why a constant took the value it took. That relocation is real, and I credit it at full size — the classical decoupling is a theorem, not a hope. The debt survives it at the same size. A value is still owed, the constant still just sits there, and at the quantum level radiative corrections take back part of the classical gift, so the value must still be chosen against the corrections rather than explained before them. I write the pricing from inside the same species of debt: my program carries a production form for the measured toll, 3Ω_Λ = 2.055, that returns the measured number exactly when fed a declared input, u(1) = 11/411, and an adopted residue, δ = 11/400 = 0.0275, carried as adopted and never derived — a declared input and a carried constant are the unimodular constant's own kind. The grade of this dead end in my census is PREMISE-ONLY, and this paper changes no headline: the vacuum catastrophe stands NOT SOLVED / PARTIAL, producing-count 0, and the toll stands NOT PRODUCED. Relocated is not retired, in their frame or in mine.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23837591
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Relocated, Not Retired: The Unimodular Integration Constant, Priced

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

Relocated, Not Retired: The Unimodular Integration Constant, Priced

William Alexander Aldred
preprint en

Abstract

This paper prices one of the cleanest moves ever made on the cosmological constant problem, and prices it without discount in either direction. In 1989 Henneaux and Teitelboim showed that in unimodular gravity the cosmological constant enters as an integration constant rather than as a coupling in the action: vacuum fluctuations decouple from the gravitational Λ at the classical level, and the question changes from why a coupling is small to why a constant took the value it took. That relocation is real, and I credit it at full size — the classical decoupling is a theorem, not a hope. The debt survives it at the same size. A value is still owed, the constant still just sits there, and at the quantum level radiative corrections take back part of the classical gift, so the value must still be chosen against the corrections rather than explained before them. I write the pricing from inside the same species of debt: my program carries a production form for the measured toll, 3Ω_Λ = 2.055, that returns the measured number exactly when fed a declared input, u(1) = 11/411, and an adopted residue, δ = 11/400 = 0.0275, carried as adopted and never derived — a declared input and a carried constant are the unimodular constant's own kind. The grade of this dead end in my census is PREMISE-ONLY, and this paper changes no headline: the vacuum catastrophe stands NOT SOLVED / PARTIAL, producing-count 0, and the toll stands NOT PRODUCED. Relocated is not retired, in their frame or in mine.

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