Saved in:
| Main Authors: | , |
|---|---|
| Format: | Recurso digital |
| Sprog: | |
| Udgivet: |
Zenodo
2026
|
| Fag: | |
| Online adgang: | https://doi.org/10.5281/zenodo.19600735 |
| Tags: |
Tilføj Tag
Ingen Tags, Vær først til at tagge denne postø!
|
Indholdsfortegnelse:
- <p>The Entropy-Response Gravity (ERG) programme has established that the Bekenstein-Hawking entropy S = A/4G, applied at the local Rindler–de Sitter horizon, uniquely determines the MOND interpolating function μ(x) = x/√(1+x²), the acceleration scale a₀ = cH₀/√(4π²−1), and the baryonic Tully-Fisher exponent α_BTFR = 4. The derivation identifies the infrared limit of the gravitational renormalisation group (RG) flow with the Wilson-Fisher (WF) fixed point of the large-N O(N) model, where the critical exponent β′(g★) = −2.<br>This paper shows that the same exponent controls two additional cosmological observables: (i) the primordial scalar spectral index n_s = 1 − 2/N_e, derived from the beta-sigma theorem and matter-radiation equality as N_e = N_total − ln(T_P/T_eq) = 57.70 ± 0.01, giving n_s = 0.9653, matching Planck 2018 to +0.10σ with zero free parameters; and (ii) the tensor-to-scalar ratio r = 0 exactly. We report a new measurement of the ERG entropy-lensing coupling using n = 289 eFEDS clusters: weak lensing mass M_WL anti-correlates with entropy K = kT/n_e^(2/3) at fixed T at slope −1.02 ± 0.08 (12.4σ); ΛCDM predicts slope = 0.<br>The total ERG flow from the Planck length to the MOND scale spans N_total = ln(c/(a₀ℓ_P)) = 122.59 e-folds. The observable CMB window N_e = 57.70 is derived in Appendix B using two established ERG results: (1) N_total = 122.59 from the Planck-to-de Sitter thermal hierarchy; (2) the beta-sigma theorem (Paper III), which proves ERG ≡ GR for T > T_eq, making the 64.90 e-folds from the Planck epoch to matter-radiation equality observationally inert. The spectral running is α_s = −2/N_e² = −6.0 × 10⁻⁴ (CMB-S4 testable). The primordial non-Gaussianity f_NL = 0 exactly in the large-N limit.<br>Five observables — α_BTFR = 4, C_O∂J = 0.474, the eFEDS entropy-lensing slope, n_s = 0.9653, and r = 0 — all follow from β′(g★) = −2, spanning 20 orders of magnitude from kpc to Gpc with zero free parameters. The r = 0 prediction is the hardest falsification criterion: any detection r > 0.001 at 5σ by CMB-S4 or LiteBIRD immediately eliminates ERG. No other published framework connects the galaxy-scale BTFR exponent to the primordial CMB spectral index through a single derived quantity.</p>