Inflation-Free Cosmology from the Bekenstein-Hawking Entropy: A Single Critical Exponent Unifies the CMB Spectral Index, the Baryonic Tully-Fisher Slope, and Gravitational-Wave Suppression
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2026
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| _version_ | 1866901526646095872 |
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| author | Margetts, David Margetts, Anthony |
| author_facet | Margetts, David Margetts, Anthony |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19600735 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Inflation-Free Cosmology from the Bekenstein-Hawking Entropy: A Single Critical Exponent Unifies the CMB Spectral Index, the Baryonic Tully-Fisher Slope, and Gravitational-Wave Suppression Margetts, David Margetts, Anthony modified gravity MOND Bekenstein-Hawking entropy spectral index inflation-free cosmology Wilson-Fisher fixed point renormalisation group tensor-to-scalar ratio baryonic Tully-Fisher relation de Sitter Rindler horizon entropy-lensing eFEDS CMB-S4 gravitational waves cosmological constant AeST ERG <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> |
| title | Inflation-Free Cosmology from the Bekenstein-Hawking Entropy: A Single Critical Exponent Unifies the CMB Spectral Index, the Baryonic Tully-Fisher Slope, and Gravitational-Wave Suppression |
| topic | modified gravity MOND Bekenstein-Hawking entropy spectral index inflation-free cosmology Wilson-Fisher fixed point renormalisation group tensor-to-scalar ratio baryonic Tully-Fisher relation de Sitter Rindler horizon entropy-lensing eFEDS CMB-S4 gravitational waves cosmological constant AeST ERG |
| url | https://doi.org/10.5281/zenodo.19600735 |