Inertia from the de Sitter vacuum: a guide for cosmologists and astrophysicists

Abstract

An expository guide, ~5,700 words, assuming general relativity and Lambda-CDM and nothing about the framework it describes. Written to be readable in an hour by a professionally sceptical reader, and structured so that the reasons to DISBELIEVE it are as easy to find as the reasons to keep reading. THE PROPOSAL. That the MOND acceleration scale is not an independent constant but a property of the de Sitter vacuum, a0 = κ c √(GρΛ) = cHΛ/Z, and that the phenomenology follows from a modification of INERTIA rather than of gravity. Two consequences a cosmologist should weigh: the scale is constant for a STRUCTURAL reason (HΛ does not evolve, so the awkwardness of tying a static galactic scale to a time-dependent H0 disappears); and Lambda-CDM has no reason to predict a relation between the dark-energy scale and the dark-matter-phenomenology scale, while this framework has no freedom to avoid it. That is the main asset, and it is NOT evidence the framework is correct. WHAT IT COVERS. The de Sitter-Unruh mechanism, with Milgrom's credit made explicit (the interpolating function ν = √(1+1/y) IS Eq. 9 of Milgrom 1999, not a variant; the framework's distinctive content is the COEFFICIENT, a factor of eleven, and it is the number that resists derivation). What modified inertia commits you to: mi ≠ mg with the weak equivalence principle INTACT (m cancels, so universality of free fall is exact) and a galaxy's gravitating mass equal to its BARYONIC mass. A parity theorem: Minkowski admits only the metric and the Levi-Civita tensor, both of EVEN rank, so every polynomial scalar in four-velocities has even degree and contributes only even powers of the orbital speed -- while deep MOND needs the FIRST power, a mismatch of (c/v)2 ~ 106-107 in amplitude. The rapidity gap is therefore FORCED, not chosen. Then the field theory in four moves: the memory kernel becomes a local critically-damped auxiliary field (so a0 = (2/3)c m2/g, a coupling ratio, and the ghost question becomes a degree-of-freedom count that closes); the preferred frame becomes a dynamical khronon (vorticity vanishes identically, the spin-1 sector is removed, and the khronon's own acceleration turns out to BE the Newtonian field); the scalar mode is healthy in an explicit window with GW170817 fixing the graviton speed as a MEASUREMENT; and MOND falls out of the joint field equations non-circularly, v4 = GMa0, with the same PPN bound that made the scalar healthy GUARANTEEING the Newtonian background modified inertia presupposes. AND A NO-GO ON THE CENTRAL NUMBER. All moments of the de Sitter worldline correlator are Mp = 21-pΓ(p+1)ζ(p)a1-p. ζ has exactly one pole, at p = 1 -- and the rapidity gap is LINEAR in the lag, which forces p = 1. The one moment the framework requires is the one moment the correlator does not have, and the same integer forbids the required √π. What survives is a reframing: a logarithmically divergent moment's finite part is a RENORMALISATION CONDITION, so a0 has the status of a Yukawa coupling. A theory is not incomplete because it has a parameter -- but it is not predictive about it either. WHAT THE GUIDE REFUSES TO CLAIM, stated in section 0 so a reader can calibrate immediately. It does not claim dark matter is dead: section 4.4 gives the strongest reason to think this framework is WRONG -- clusters, at +0.405 dex and 2.0-4.1 sigma on the framework's OWN kernel, with the discrepancy GROWING INWARD across a 3x-24x ladder, the weak-lensing recalibration helping to ~1.6-1.8 without closing it, and an earlier claim that X-ray calorimetry closed it explicitly WITHDRAWN. It is not a theory of everything, and the specific obstruction is named: the framework's characteristic constant carries √π while all flavour observables are algebraic, so the relevant structure is BLIND to the gauge sector. And it does not derive a0. AGAINST INTEREST, throughout rather than in a footnote. The radial acceleration relation is convention-COMPATIBLE and NON-DIAGNOSTIC of the coefficient (0.108 dex, better than regularised MOND's 0.122, but the penalty for moving a0 by 20% is under half a per cent) and two of the author's own claims about it were withdrawn for exactly that reason. The baryonic Tully-Fisher intercept is mass-to-light degenerate. The 2.2 sigma coefficient discrimination does NOT survive the interpolation-kernel change -- it flips to 0.66 sigma the other way. Both dimensionless constants that appear naturally in the construction are 2π, which is Milgrom's value: THEORY prefers his coefficient while DATA prefers this one, at 2.2 sigma, and that tension is unresolved. The covariantisation ADDED two free parameters, so the scalar's health is achieved BY CHOICE rather than predicted. A 2026 measurement of a0 rising with redshift is a TENSION with the predicted bump-then-decline, not a confirmation, and a contrary analysis that dropped wa in a low-redshift expansion is named as withdrawn. Both power-law interpolation kernels are excluded by planetary ranging. And the pre-registered wide-binary test can disfavour the framework decisively and can support it only weakly: one number with teeth (a Newtonian result is evidence against at 4.74-7.10 sigma) against a scoring-bin collision, a nuisance outside its frozen window, an unscoreable corner, and two further checks underpowered at the registered sample size. AND THE ERROR RATE, in section 10 rather than hidden. On the single day the field theory was assembled, SIX load-bearing claims were drafted, checked and found wrong -- a past-directed sign convention, an invariance argument that assumed its own conclusion, an asserted observational band replaced by a computed one, an overstated limitation, a claimed cutoff that did not clear collider energies at all powers, and a ratio quoted as exact when its coefficient was three -- plus one check that passed VACUOUSLY on an empty list before being caught. Each is named. Every quantitative claim is generated by a script that exits non-zero on failure and carries controls designed to trip, and where those scripts contradicted the author, the author lost. CREDIT. Milgrom 1999 PLA 253:273 (the mechanism and the interpolating function) and Milgrom 1994 Ann.Phys. 229:384 (generic time-nonlocality of modified inertia); Deser & Levin 1997 CQG 14:L163; Bekenstein & Milgrom 1984 ApJ 286:7; Gibbons & Hawking 1977; Bunch & Davies 1978; Narnhofer, Peter & Thirring 1996; Horava 2009; Jacobson & Mattingly 2001; Jacobson 2010; Blas, Pujolas & Sibiryakov 2010, 2011; Blas & Sibiryakov 2011 (universal horizons); Israel & Stewart 1979; Elliott, Moore & Stoica 2005; McGaugh, Lelli & Schombert 2016 and McGaugh 2012; Banik et al. 2024; El-Badry, Rix & Heintz 2021. AI-assistance disclosure. Portions of the analysis, numerical verification and drafting were carried out with the assistance of a large language model (Anthropic Claude). The author directed the work, specified and reviewed every load-bearing calculation, and takes full responsibility including for any errors. No AI system satisfies the criteria for authorship and none is listed as an author. Reproducibility. Six of the technical spine's scripts are included (30/30, 27/27, 26/26, 30/30, 32/32 and 30/30 checks); the remainder live in the deposits cited above. Both a0 footings are carried on every dimensionful number.