Self-consistent inflationary trajectory in the Triptyque Conceptuel: n_s=0.9649, spectral closure, and modified tensor-to-scalar consistency relation
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2026
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| _version_ | 1866901380971626496 |
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| author | Nédélec, Yann |
| author_facet | Nédélec, Yann |
| contents | <p><span>DESCRIPTION — NOTE V10</span></p> <p>This companion note provides a concise self-contained summary of the three central results of Triptyque Conceptuel version 10 (DOI: 10.5281/zenodo.19389437).</p> <p> </p> <p>(i) The inflationary background equation of motion σ_NN + (3−ε)·σ_N + V’/H² = 0, where V(σ) = Ω²(σ)·[T_Q + m²σ²], admits a universal slow-roll attractor independent of the initial condition σ₀. On this attractor, n_s = 1 − 6ε_V + 2η_V = 0.9649 at N = 57.1 e-folds before the P10 threshold (Λ = 4), compatible with the Planck 2018 measurement (0.9649 ± 0.0042).</p> <p> </p> <p>(ii) The constraint P_s = 2.1×10⁻⁹ (Planck 2018) fixes the unique free parameter of the model: m_phys = 1.585×10⁻³ M_Pl and T_P10 = 7.924×10⁻⁴ M_Pl. The model is thereby reduced to zero free parameters once P_s is imposed.</p> <p> </p> <p>(iii) A modified tensor-to-scalar consistency relation is established: r = κ_phys = 3·m²_phys = 7.5×10⁻⁶, differing from the standard slow-roll result r = 16·ε_V = 0.140. The Triptyque prediction is compatible with current bounds (r < 0.034, 2025 datasets), whereas the standard value is not. The modified relation r ≠ −8·n_t (with n_t = −0.0175) constitutes a falsifiable prediction in principle testable by future CMB polarisation experiments.</p> <p> </p> <p>The central open question for version 11 is the formal derivation of the canonical perturbative variable z in the effective geometry g_eff = Ω²(σ)·η.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19389851 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Self-consistent inflationary trajectory in the Triptyque Conceptuel: n_s=0.9649, spectral closure, and modified tensor-to-scalar consistency relation Nédélec, Yann self-consistent inflationary trajectory slow-roll attractor scalar spectral index tensor-to-scalar ratio modified consistency relation spectral closure cosmic microwave background CMB polarisation primordial power spectrum Madelung decomposition Triptyque Conceptuel <p><span>DESCRIPTION — NOTE V10</span></p> <p>This companion note provides a concise self-contained summary of the three central results of Triptyque Conceptuel version 10 (DOI: 10.5281/zenodo.19389437).</p> <p> </p> <p>(i) The inflationary background equation of motion σ_NN + (3−ε)·σ_N + V’/H² = 0, where V(σ) = Ω²(σ)·[T_Q + m²σ²], admits a universal slow-roll attractor independent of the initial condition σ₀. On this attractor, n_s = 1 − 6ε_V + 2η_V = 0.9649 at N = 57.1 e-folds before the P10 threshold (Λ = 4), compatible with the Planck 2018 measurement (0.9649 ± 0.0042).</p> <p> </p> <p>(ii) The constraint P_s = 2.1×10⁻⁹ (Planck 2018) fixes the unique free parameter of the model: m_phys = 1.585×10⁻³ M_Pl and T_P10 = 7.924×10⁻⁴ M_Pl. The model is thereby reduced to zero free parameters once P_s is imposed.</p> <p> </p> <p>(iii) A modified tensor-to-scalar consistency relation is established: r = κ_phys = 3·m²_phys = 7.5×10⁻⁶, differing from the standard slow-roll result r = 16·ε_V = 0.140. The Triptyque prediction is compatible with current bounds (r < 0.034, 2025 datasets), whereas the standard value is not. The modified relation r ≠ −8·n_t (with n_t = −0.0175) constitutes a falsifiable prediction in principle testable by future CMB polarisation experiments.</p> <p> </p> <p>The central open question for version 11 is the formal derivation of the canonical perturbative variable z in the effective geometry g_eff = Ω²(σ)·η.</p> |
| title | Self-consistent inflationary trajectory in the Triptyque Conceptuel: n_s=0.9649, spectral closure, and modified tensor-to-scalar consistency relation |
| topic | self-consistent inflationary trajectory slow-roll attractor scalar spectral index tensor-to-scalar ratio modified consistency relation spectral closure cosmic microwave background CMB polarisation primordial power spectrum Madelung decomposition Triptyque Conceptuel |
| url | https://doi.org/10.5281/zenodo.19389851 |