Khronon Weak-Field Generality: 12 Independent Tests, Zero Free Parameters

In the deep MOND limit, M_bar = V_f⁴ / (G a₀). The slope 4 is an exact analytic result with zero adjustable parameters. The intercept is fixed by a₀ = cH₀/(2π).

NFW halo models predict slopes 3.0–3.5 depending on halo concentration and feedback prescriptions. The exact value is not predicted a priori.

Full SPARC sample: 3.85 ± 0.09. Gas-dominated (clean) subsample: 3.68 ± 0.12. The slope is consistent with 4 within systematics of M/L calibration.

A universal deterministic formula g_obs(g_bar) implies that residual scatter comes only from measurement errors (distance, inclination, M/L). This scatter should be constant across all accelerations.

In CDM, the RAR arises statistically from halo abundance matching. Scatter should increase at low accelerations where halo diversity is greatest.

SPARC data shows 0.17–0.19 dex scatter that is flat across all acceleration bins from 10⁻⁹ to 10⁻¹² m/s². Measurement floor is ~0.12 dex, so most scatter is observational.

When g_bar ≪ a₀, the interpolating function asymptotes to g_obs = √(g_bar · a₀). The ratio g_obs/√(g_bar a₀) should approach exactly 1.

Using the lowest acceleration bins of SPARC galaxies (g_bar < 10⁻¹¹ m/s²), the ratio is measured to be 1.04 — within 4% of the exact prediction.

Modified gravity predicts that the effective circular velocity remains approximately flat out to ~1 Mpc, yielding V_circ ~ 195 km/s for an L* galaxy. There is no dark halo edge to cause a Keplerian decline.

NFW halos have a virial radius of ~200–300 kpc. At 1 Mpc, well beyond the halo, the velocity should decline as r^−1/2, giving only ~66 km/s.

Mistele et al. (2024) used weak gravitational lensing to measure the effective potential profile of isolated galaxies out to ~1 Mpc. The profile remains flat, strongly favoring the modified gravity prediction.

Tidal dwarf galaxies (TDGs) form from material stripped in galaxy interactions. They cannot capture a dark matter halo. In modified gravity, their rotation curves follow directly from their baryonic mass: V_flat ~ 35 km/s for typical TDGs.

Without a dark halo, TDGs should show only baryonic circular velocities (~15 km/s). Observed velocities of 30–40 km/s require either dark matter (impossible for TDGs) or modified gravity.

Three TDGs in the NGC 5291 system show V = 30–40 km/s, consistent with modified gravity and a factor ~2 above Newtonian expectation.

Using the Khronon interpolating function with a₀ = 1.13 × 10⁻¹⁰ m/s² and the known baryonic mass of the Milky Way, the predicted escape velocity at the solar radius is 558 km/s. No halo model is needed.

Gaia DR3 data yields v_esc = 530–580 km/s at the solar position. The Khronon prediction sits in the middle of this range.

Without a massive dark halo, bars experience minimal dynamical friction. The ratio R = R_CR/R_bar should be 1.0–1.3 (fast bars).

Dark matter halos produce dynamical friction that slows bars. N-body simulations consistently produce R ~ 1.7 (slow bars), regardless of feedback prescriptions.

Tremaine-Weinberg measurements show 72% of observed bars are fast (R < 1.4). This is a persistent and well-documented failure of CDM simulations.

In modified gravity, the Toomre parameter Q_MOND for low surface brightness (LSB) galaxies hovers near 1, allowing the observed spiral structure and star formation. This is the marginally stable regime expected for real disks.

Massive dark matter halos dominate the potential in LSB galaxies, yielding Q ~ 2.8. Such disks are overstabilized and should not form spiral arms or show significant star formation — contradicting observations.

Wide binary stars at separations of 5–10 kAU probe accelerations near a₀. Because they are embedded in the Milky Way's external field, the gravitational boost is suppressed (EFE) to 8–13% above Newtonian.

Chae (2024) analyzed Gaia wide binary data and found a gravitational anomaly at large separations consistent with the MOND EFE prediction. Hernandez et al. (2024) independently confirm the signal.

The lensing power-law index β for the Khronon exponential metric gives β = 6.2. This is 2.4σ from the observed value — the closest of any theory.

NFW profiles predict β = 8.0, which is excluded at 6.8σ by the SLACS strong lensing data.

Fagin et al. (2024) measured β = 5.22 ± 0.41 from SLACS strong lens systems. CDM is decisively excluded; Khronon is the closest match among tested theories.

Of the 20 worst-fit dwarf irregulars, 13 are overpredicted even with stellar mass-to-light ratio M/L = 0 (i.e., even zero stellar mass overpredicts the rotation speed). This means the HI gas mass alone exceeds what is needed, indicating either distance errors or non-circular motions dominate the residuals. This is a data quality problem affecting all gravity theories equally, not a specific failure of modified gravity.

Globular clusters (GCs) sit deep in the Milky Way's potential well, so Σ_GC/Σ_MW ≪ 1. The Σ-hierarchy predicts that GCs should behave nearly Newtonian — modified gravity effects are suppressed, not absent.

Naive MOND (ignoring the external field / Σ-hierarchy) gives RMS velocity dispersion errors of ~186%. Applying the Σ-hierarchy correction reduces this to ~33%. The remaining residual may come from tidal effects and anisotropy in GC velocity dispersions.

The Σ-hierarchy is NOT the same as MOND's external field effect (EFE). It arises from the relative entropy structure Σ = D(ρ_spacetime || ρ_matter) and determines whether a subsystem “sees” modified gravity at all.