Reframing the Cosmological Constant: Λ as an Integration Constant, Not a Vacuum Energy — Unimodular Gravity and the +C Duality of Paper 62.
The cosmological constant problem is usually stated as a fine-tuning: the QFT vacuum energy density exceeds the observed Λ by up to ~10¹²⁰, so a bare constant must cancel it to that precision. This presupposes that vacuum energy sources Λ. This paper develops the reading of Paper 62 — Λ canonically conjugate to the 4-volume V₄, dual to the volume-baseline integration constant +C of Paper 12 — into a reframing via unimodular gravity. There the metric determinant is fixed and the field equations are trace-free; a constant vacuum energy is pure trace and so does NOT source them. The effective cosmological constant re-emerges as a constant of integration, conjugate to V₄ (Henneaux–Teitelboim 1989). Thus Λ is boundary data, not a computed vacuum energy, and the “120 orders” is a CATEGORY ERROR: it compares a vacuum energy with a boundary datum the theory does not identify. IMPORTANT LIMIT: unimodular gravity removes the radiative fine-tuning but does NOT predict Λ; the observed smallness becomes a boundary-condition question. As the model of a disciplined structural prediction we hold up Sorkin’s causal-set argument that Λ ~ ±1/√V₄ ~ H₀² — from the same Λ–V₄ conjugacy — which anticipated the observed order of magnitude before 1998. No new physics; this is a reframing (emergent-gravity neighbourhood), not a solution.
A note on the aim of this work. This is a structural interpretation and reframing of a known problem using established (non-string) unimodular gravity, not a solution and not a new physical law. Nothing here is intended to contradict existing results.
On the making of this work: The ideas and content of this work stem from the author’s own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author’s. Feedback and corrections are sincerely appreciated.
Reference
Yamagishi, Y. (2026). Reframing the Cosmological Constant: $\Lambda$ as an Integration Constant, Not a Vacuum Energy (Unimodular Gravity and the $+C$ Duality of Paper 62) [Paper 72]. Zenodo.
DOI: 10.5281/zenodo.21650934
ORCID: 0009-0006-8587-3450