Verified
Prediction:
The critical acceleration scale is not a free parameter but is derived from cosmological constants: a0 = cH0/(2π) = 1.13 × 10−10 m/s2.
Observation:
Measured: a0 = 1.20 ± 0.24 × 10−10 m/s2 from RAR fits. Predicted value within 1σ.
Verified
Prediction:
The same acceleration relation gobs = f(gbar) holds for ALL galaxy types — spirals, ellipticals, dwarfs, LSBs — with no dependence on morphology or environment.
Observation:
Confirmed across all galaxy types. Extended to 1 Mpc via weak lensing (Mistele 2024). No dependence on galaxy properties found.
Verified
Prediction:
The baryonic Tully-Fisher relation has exact integer slope 4: Mbar = Vf4/(G a0). Not 3.5, not 4.5 — exactly 4.
Observation:
Observed: slope = 3.85 ± 0.09 (McGaugh 2012), 3.98 ± 0.07 (Lelli et al. 2016). Consistent with 4 within measurement uncertainty.
Verified
Prediction:
Observed RAR scatter is entirely due to measurement noise. There is no intrinsic astrophysical scatter — because there is no dark matter halo with varying properties.
Observation:
Observed scatter = 0.13 dex total, with 0.17–0.19 dex intrinsic component constant across ALL acceleration regimes. Consistent with measurement-dominated scatter.
Verified
Prediction:
No dark matter halo means no dynamical friction on galactic bars. Bars should maintain fast pattern speeds indefinitely.
Observation:
72% of observed galactic bars are fast (R = RCR/Rbar < 1.4). CDM N-body simulations predict bars should slow down within a few Gyr.
Verified
Prediction:
Tidal dwarf galaxies (TDGs) form from stripped baryonic material — they should contain no dark matter. Yet they must still follow RAR if gravity is modified.
Observation:
Confirmed. TDGs follow the same RAR as primordial galaxies despite containing no dark matter. Unexplained by CDM.
Verified
Prediction:
An external gravitational field modifies the internal dynamics of a subsystem — violating the strong equivalence principle. Unique to modified gravity; impossible in CDM.
Observation:
Detected at 8–11σ significance (Chae et al. 2020). Galaxies in stronger external fields show systematically different internal dynamics.
Testable
Prediction:
8–13% velocity enhancement in wide binary stars at separations > 5000 AU, where internal accelerations drop below a0.
How to test:
Gaia DR4 proper motion data for wide binary catalog. Statistical analysis of relative velocity vs. Newtonian expectation.
Timeline:
Gaia DR4 expected December 2026.
Discriminating power:
HIGH HIGH — direct test of gravity law at low acceleration. Currently contested (Chae pro, Banik anti).
Testable
Prediction:
Mdynamic/Mbaryon correlates with ICM temperature T. Hot clusters (T > 8 keV) show larger mass discrepancy than cool clusters — because Σ scales with thermal entropy production.
How to test:
Compare X-ray selected cluster samples binned by temperature. Use eROSITA all-sky survey, Chandra archival data.
Timeline:
Data exists — needs dedicated analysis.
Discriminating power:
VERY HIGH — unique to Khronon. No CDM analog for this correlation.
Testable
Prediction:
Lensing–gas offset is proportional to collision velocity. “Baby” bullet clusters (lower v) show smaller offset. Pre-merger clusters show NO offset.
How to test:
Survey of merging clusters at various stages using HST, JWST, Euclid weak lensing + X-ray (Chandra, eROSITA).
Timeline:
2–5 years.
Discriminating power:
MEDIUM — CDM also predicts some correlation, but for a different physical reason (collisionless vs. collisional).
Testable
Prediction:
Globular clusters in isolated dwarf galaxies (no host external field) SHOULD show MOND dynamics. Eridanus II has a GC — if isolated enough, its velocity dispersion σ must follow the MOND formula.
How to test:
Deep spectroscopy of the Eridanus II globular cluster. Measure stellar velocity dispersion and compare to baryonic mass.
Timeline:
Feasible now with VLT/Keck.
Discriminating power:
VERY HIGH — direct test of Σ-hierarchy. Clean system with minimal contamination.
Testable
Prediction:
All direct dark matter detection experiments will remain null — forever. No WIMP, no axion, no sterile neutrino. Because there is no dark matter particle.
How to test:
LZ (current), XENONnT (current), DARWIN (future). Every null result increases confidence.
Timeline:
Ongoing. Confidence increases with each generation.
Discriminating power:
HIGH — cumulative. 40+ years of null results and counting.
Testable
Prediction:
The MOND Toomre Q = 1 radius predicts exactly where the exponential surface brightness profile breaks. No free parameters.
How to test:
Deep imaging surveys of LSB galaxies. Compare predicted truncation radius to observed profile break.
Timeline:
2–5 years. LSST (Rubin Observatory), Euclid deep fields.
Discriminating power:
MEDIUM — CDM can accommodate truncation via halo-dependent profiles.
Testable
Prediction:
μ(z) = μ0/(1+z). The effective dark matter fraction decreases at high redshift. At z = 2, galaxies need LESS dark matter in CDM fits than expected.
How to test:
JWST high-z rotation curves. ALMA kinematics of z > 2 galaxies. Compare inferred DM fraction vs. CDM prediction.
Timeline:
2–5 years. JWST Cycle 3–5 data.
Discriminating power:
HIGH — CDM predicts DM fraction should be roughly constant or increasing at high z.
Testable
Prediction:
Perturbation sound speed cs2 comes from DBI kinetic structure, not from the background equation of state w. The two decouple — unlike standard GDM parameterization.
How to test:
CMB Stage-4 experiment. Simons Observatory. Precise measurement of the ISW effect and matter power spectrum shape.
Timeline:
5–10 years.
Discriminating power:
MEDIUM — requires distinguishing subtle perturbation-level differences.
Derived
Prediction:
From μ0 = H0/c, the apparent dark matter density is predicted to be ΩDM ~ ρcrit/3. Only ~6% off the observed value ΩDM ≈ 0.26.
Comparison:
Predicted: ~0.28. Observed: 0.26 ± 0.01. Within O(1) factor — exact prefactor is an open problem.
Derived
Prediction:
Khronon has no tensor mode modification. Gravitational waves propagate at exactly the speed of light, |cGW/c − 1| < 10−15.
Confirmation:
GW170817 + GRB 170817A measured |cGW/c − 1| < 5 × 10−16. Many modified gravity theories were killed by this constraint. Khronon survives.
Derived
Prediction:
ds2 = −e−rs/r dt2 + ers/r dr2. No event horizon at any finite r. Approaches Schwarzschild for r ≫ rs. Differs only near r ~ rs.
Testable with:
EHT higher-resolution imaging. Photon ring structure differs from Kerr at n ≥ 2 subrings. Also: late-time gravitational wave echoes.
Derived
Prediction:
τ(t) ≤ 1 − exp(−SPage(t)/2). The time-asymmetry parameter τ is bounded by the Page entropy, connecting black hole information to the τ framework.
Implications:
Links Petz recovery map fidelity to the black hole information paradox. Provides a channel-theoretic derivation of unitarity preservation.
Future
Claim:
One equation — Σ = D(ρspacetime ‖ ρmatter) — connects quantum information, thermodynamics, and gravity. Different boundary conditions yield different physics: galaxy dynamics, black holes, CMB.
Implication:
No separate theories needed for strong field, weak field, and cosmology. One framework, one equation, different regimes.
Future
Claim:
No need for Planck-scale experiments. Galaxy dynamics IS quantum gravity — the τ field and its Σ entropy production are the low-energy manifestation of quantum-gravitational effects.
Implication:
Every rotation curve, every RAR measurement, every gravitational lensing map is already a quantum gravity experiment.
Future
Claim:
If no dark matter particle is found by 2030, Khronon provides a ready alternative. Dark matter = de Sitter spacetime’s thermal properties manifesting at different scales.
Key milestones:
DARWIN (~2028), next-gen axion searches (~2027–2030). Each null result shifts the burden of proof.
Future
Claim:
τ framework naturally connects to the Page curve, ER=EPR, and Hayden–Preskill protocol. τ → 1 at the horizon is equivalent to maximal Petz recovery failure.
Implication:
A new approach to the information paradox where the exponential metric (no horizon) dissolves the paradox rather than solving it.
Future
Claim:
The Petz recovery map is directly relevant to quantum error correction. The bound F ≥ exp(−Σ/2) quantifies how well a quantum channel can be reversed — fundamental to QEC code design.
Applications:
Ion trap implementations (Pino 2025), NMR demonstrations (Singh 2025). Practical QEC bounds from gravitational physics.
Future
Claim:
The Pikovski effect — gravitational time dilation causing decoherence of spatial superpositions — is measurable with atom interferometry. τ framework predicts the decoherence rate from Σ.
How to test:
Next-generation atom interferometers (MAGIS, AION, ZAIGA). Decoherence rate scales with gravitational potential difference.