Why the Bare Cosmological Constant Vanishes
Five convergent proofs from entanglement entropy
Eliminates the last assumption of the cosmological constant derivation: Λ_bare = 0 is derived, not assumed. Five independent arguments — QNEC completeness, spectral trace identity, modular Hamiltonian structure, CHM mechanism, and functional completeness — all converge on the same conclusion.
Mar 9, 2026 · Preprint
Plain English
This paper proves that vacuum energy does not generate a separate cosmological constant — because it was already gravity all along.
The problem
The companion paper derived dark energy from quantum entanglement, but had to assume that the "bare" cosmological constant — the contribution from vacuum energy — is zero. Without this assumption, you just get an unconstrained sum and the prediction is lost. This is the original cosmological constant problem: vacuum energy should make the universe expand 10¹²² times faster than it does.
The key idea
The entanglement entropy of a region has a second derivative S''(n) with exactly two terms: a constant and a 1/n² correction. These map one-to-one to the two gravitational constants G and Λ. There is literally no mathematical room for a third constant Λ_bare. The vacuum energy is not missing — it is already encoded in the area-law term that determines Newton's constant.
What the paper does
It presents five independent proofs, each using different mathematics: (1) QNEC completeness — S''(n) has exactly two parameters, both spoken for; (2) spectral trace identity — tr(P_sub)/ρ converges to 1.000000000000 under Richardson extrapolation; (3) modular Hamiltonian — 97% spectral overlap with physical Hamiltonian, 100% for the entropy-carrying mode; (4) CHM mechanism — geometric kernel converts volume-law energy into area-law entropy; (5) functional completeness — the hidden perimeter term drops out of the field equations.
Why it matters
This completes the zero-parameter derivation of the cosmological constant. The full chain — Standard Model field content → entanglement entropy → (G, Λ) with no bare cosmological constant — gives Λ_pred/Λ_obs = 0.9999. The bound on any residual bare contribution is |Λ_bare|/Λ_ent ≲ 10⁻⁷⁴. The 122-order-of-magnitude puzzle is resolved: vacuum energy was never missing, it was gravity.
What could go wrong
All arguments work within the entropic gravity framework (Jacobson's thermodynamic derivation of Einstein's equations). If gravity is fundamental rather than emergent, the arguments do not apply. The spectral trace identity and modular Hamiltonian results are verified on a free-field lattice; extension to interacting theories requires further work. This is a preprint and has not been peer-reviewed.