A-phase (V9.0 closure): the CMB-background question for geometric DM

Status: V9.0 auditor finding, quarantined (NOT V8.2, NOT theory, NOT PDF). June 2026. Romain’s “attack A”, task (1): is the closure wall (b) — the CMB BACKGROUND — fatal, or can a halo-free homogeneous a⁻³ sector exist? Mode: reviewer/auditor, prudence BOTH ways (test, don’t glue — and self-correct when a first pass over-states). Companions: QUBIT_HOLOGRAPHY_NOTE.md (the inflation-entanglement thread), a_closure_cmb.py (the z_eq numbers).

The requirement

The CMB acoustic peaks need a homogeneous a⁻³ matter component ~5× baryons (Ω_m h²≈0.143) so that matter-radiation equality z_eq=Ω_m h²/Ω_r h²−1≈3400 puts recombination (z≈1090) in the matter era (constant potentials → the observed peak heights). Whatever plays the DM must (i) be homogeneous + a⁻³ for z_eq, (ii) cluster on ~100 Mpc at recombination to source the wells, and (iii) stay halo-free in galaxies to preserve OBT’s MOND rotation curves. (i)+(iii) is the MOND-CMB tension.

Three scenarios (a_closure_cmb.py)

• S1 — Weyl as the background DM: FAILS. The projected Weyl E_μν is traceless (Shiromizu-Maeda- Sasaki) ⇒ a homogeneous isotropic Weyl has w=1/3 (radiation, a⁻⁴), not a⁻³ matter. Matter = baryons only ⇒ z_eq≈535 ⇒ recombination in the radiation era ⇒ grossly wrong peaks. The inhomogeneous (geometric) Weyl is mean-zero ⇒ 0 contribution to H(z). So the Weyl cannot be the CMB background DM.
• S2 — radion condensate (a⁻³, Gate 10 misalignment, Ω_cond h²≈0.12 at φ₀=M_s): does z_eq, breaks galaxies. With baryons + condensate, Ω_m h²≈0.142 ⇒ z_eq≈3407 ⇒ recombination in the matter era ✓. But Gate 11: the 0.36 eV condensate clusters into galaxy halos ⇒ kills the zero-halo MOND success. So the wall is not “no a⁻³ background” — it is the a⁻³ sector’s galactic clustering (the tension).
• S3 — AeST (Skordis-Złošnik 2021, PRL 127, 161302): the resolution exists. A relativistic-MOND scalar whose homogeneous energy density behaves as dust (a⁻³) → fits the Planck CMB + matter power spectrum, while giving MOND (halo-free) in galaxies. Proof by construction that the MOND-CMB tension is surmountable by a single field.

Self-correction (prudence both ways)

My first pass tested only S1 (“Weyl-only”) and called the CMB an almost-fatal structural wall. That over-stated it. OBT has S2 (a real a⁻³ candidate that pays the z_eq bill), and S3 proves the tension is surmountable in principle. The honest statement is narrower and sharper: the Weyl cannot be the background DM (a⁻⁴); the only open problem is finding a halo-free a⁻³ sector — which is known to be possible (AeST).

Verdict

• The CMB is not a proven-fatal wall for OBT. What is solid: the Weyl alone cannot supply the homogeneous a⁻³ background (tracelessness). What is open but surmountable: a halo-free a⁻³ sector (AeST exists; OBT must realize it).
• OBT’s concrete A target: realize the AeST mechanism inside the bulk — a shift-symmetric radion / brane-bending mode that is a⁻³ dust cosmologically AND MOND/halo-free galactically. The massive 0.36 eV condensate is not it (clusters, Gate 11); the Weyl is not it (a⁻⁴). OBT already gets a₀=cH/2π + μ(x) from the radion/bulk MOND sector — the question is whether that same sector carries an AeST-class dust mode. Mapping now DONE (a_radion_aest.py): it FAILS. AeST’s halo-free a⁻³ dust is the conserved charge of a massless, shift-symmetric scalar. OBT has no such mode: the radion is massive (0.36 eV, Goldberger-Wise — required for extra-dim stabilization + the KK spectrum), so its a⁻³ is an axion-like condensate that clusters (de Broglie ≈ 0.8 mm ≪ kpc; ~22-23 orders above the fuzzy ~10⁻²³ eV threshold) = the Gate-11 galaxy-halo result; the Weyl is a⁻⁴; the KK are massive. The radion mass is structurally incompatible with the AeST shift symmetry. ⇒ OBT does NOT inherit AeST’s CMB fit.
• Honest fallback — now the DEFAULT (the mapping failed): OBT’s position is a hybrid (geometric Weyl for galaxies/clusters + a homogeneous, ~shift-symmetric/screened sector for the CMB background) — to be stated openly, at the cost of “DM is purely geometric”. The geometric win stays at galaxy/cluster scales (where OBT is strong); the CMB needs an added homogeneous sector that OBT’s current field content does not supply.

How this relates to the qubit thread

The qubit/inflation-entanglement thread addresses the perturbation spectrum (clustering, Gate 7). It is orthogonal to (and moot until) the background question here is settled: there is no point predicting the δE_μν spectrum from inflation if the homogeneous a⁻³ sector that the CMB needs is not identified. So the ordering is: first settle the AeST-mode mapping (this note), then the inflation perturbation chain.

Next steps

1. The AeST mapping (the make-or-break) DONE (a_radion_aest.py): the mapping FAILS — OBT has no massless shift-symmetric scalar (the radion is massive → its a⁻³ condensate clusters; the Weyl is a⁻⁴). So OBT does not inherit AeST’s CMB fit → the hybrid is the honest default. Open sub-question for a future turn: can a shift-symmetric brane-bending Goldstone survive with MOND-screening instead of a hard Goldberger-Wise mass (so it is halo-free a⁻³ dust)? This conflicts with the KK spectrum + stabilization as currently built — likely a major reformulation, not a free inheritance.
2. Quantitative confirmation (task 2): an MG-CMB Boltzmann solve (CLASS/CAMB + brane + a homogeneous a⁻³ sector) to turn z_eq into an actual peak prediction — now framed for the hybrid (the added sector), since OBT’s native fields do not supply it.
3. The inflation-entanglement perturbation chain — moot for the background; still relevant for the clustering spectrum if the hybrid’s homogeneous sector is fixed.

Task (1) result (a_radion_reformulation.py): the Goldstone-screened reformulation FAILS too

The only escape from the hybrid would be to make the radion itself the AeST field (massless, shift-symmetric, halo-free a⁻³ dust) instead of a massive Goldberger-Wise radion. It fails on both horns, because the radion is the extra-dimension modulus (it sets G + the masses via the warp):

• Stabilized (massive, the actual radion): its a⁻³ condensate clusters (de Broglie ≈ 0.8 mm ≪ kpc) → galaxy halos (Gate 11) → not halo-free.
• Rolling (massless, AeST-like): carrying Ω_DM as dust needs Δφ ~ √Ω_DM·M_Pl ~ 0.5 M_Pl over a Hubble time → Δ(lnG) ~ 0.5 → Ġ/G ~ 0.5 H₀ ~ 3.5×10⁻¹¹/yr, ~350× the LLR bound (10⁻¹³/yr) → ruled out (only worse for a warp-enhanced coupling).
• Structural root: OBT’s MOND is geometric (a₀=cH/2π horizon + Weyl a⁻⁴), not a scalar field (a⁻³ dust). The geometric origin — OBT’s distinctive a₀=cH/2π — is exactly why it cannot do AeST’s one-field (MOND + a⁻³ dust) trick.

⇒ The hybrid is confirmed as the honest default. OBT is modified-gravity-for-galaxies/clusters (its geometric wins — a₀=cH/2π, μ(x), sinc, Bullet 150 kpc, the cluster two-scale anatomy — all UNAFFECTED) plus an added homogeneous a⁻³ sector for the CMB that its native fields do not supply. “DM is purely geometric” holds up to cluster scales, not at the CMB. (Loop discipline: two clean re-read passes + a re-run; a √Ω_DM refinement to Horn B and a kpc→nm units bug were caught on re-read.)

Verification of the escapes (Romain: “cherche la vérité”; web-confirmed June 2026, a_verify_options.py)

Before accepting the hybrid, the dismissed escapes were verified, not asserted:

• FACT 1 (web): modified gravity ALONE fails the CMB. TeVeS / relativistic MOND without a dark-matter-like component cannot fit the CMB third acoustic peak (over-enhanced ISW; “acceptable fits to the CMB in TeVeS still need to appeal to non-baryonic mass”). ⇒ OBT’s geometric MOND (a⁻⁴ Weyl) would fail the same way → the homogeneous a⁻³ dust is genuinely required. (physicsworld; astroweb ssm/mond/CMB6)
• FACT 2 (web): the resolution is a FIELD, not a particle. AeST (Skordis-Złošnik 2021): “the time-dependent term behaves like gravitating dust, allowing AeST to reproduce the CMB … while retaining a MOND limit”. So the added a⁻³ dust can be a scalar-tensor gravity-sector field. (aanda AeST; MNRAS 531/272)
• FACT 3 (web+calc): a natural string/fuzzy axion is NOT halo-free. Fuzzy DM “produces flat halo cores” → it clusters. To be all the DM it needs m_a > ~10⁻²¹ eV (Lyman-α); at that mass its de Broglie core is ~10 pc ≪ galaxy → it makes galaxy halos → double-counts with the MOND phantom → breaks the zero-halo galaxies. Halo-free needs m_a < ~10⁻²⁴ eV — ~3 orders below the all-DM floor → no overlap. (ar5iv 1609.09414)

Escape table — every natural OBT field fails as the CMB a⁻³ dust: Weyl (a⁻⁴), massive radion (clusters), rolling radion (varies G, ~350× LLR), KK gravitons (massive→cluster), string/fuzzy axion (cored halos / ruled out). ⇒ the hybrid is CONFIRMED by verification, not a lazy default.

The verified nuance (and it is good for OBT): because the AeST dust is a gravity-sector FIELD (not a WIMP), “DM is gravitational/geometric” (no particle dark matter) survives — OBT only needs a V9.0 extension (a new AeST-class gravity scalar) that its V8.2 fields do not supply, while the galaxy/cluster geometric wins are untouched. A’s honest end-state: OBT’s galaxy/cluster DM is the geometric Weyl + the MOND phantom (its strength), and its CMB needs an added gravity-sector a⁻³ field — a precise, verified scope, not a defeat.

(1)-deep: does OBT’s bulk NATURALLY contain the AeST/Khronon fields? (a_obt_aest_content.py)

Could the CMB sector be a free inheritance from OBT’s existing fields? No.

• Aether (unit-timelike vector): OBT’s natural vector is the brane normal n^μ, which is spacelike (the extra dimension), not timelike → not the aether. But the Khronon route (Blanchet-Marsat 2011; Blanchet 2024, JCAP11(2024)040) gets MOND + the CMB with a scalar foliation alone, no aether vector — so the aether is not the obstacle.
• Khronon (preferred-time scalar): OBT’s radion ∂_μφ does define a preferred time → structurally a khronon candidate. But the khronon/MOND scalar is ~massless (its scale is the cosmological/MOND scale ~H₀ ~ 10⁻³³ eV, via the shift-symmetric k-essence function, not a mass), whereas OBT’s radion is a hard 0.36 eV Goldberger-Wise modulus — ~32 orders too heavy, and the GW mass breaks the shift symmetry the khronon needs. The radion is the right type (a preferred-time scalar) but the wrong field.

⇒ OBT does NOT naturally contain the AeST/Khronon structure, so the V9.0 extension is now precisely named: a new ~massless (~H₀-scale) shift-symmetric khronon scalar (a gravity-sector field — no aether needed), NOT the radion (32 orders too heavy) and NOT the spacelike normal. This confirms the hybrid/added-gravity-scalar conclusion from the field-content side, and pins exactly what V9.0 must build.