The Stratoverso Framework: A Non-Perturbative Extension of Scalar Field Cosmology within General Relativity

We present the Stratoverso Framework, a non-perturbative cosmological model in which the observed accelerated expansion of the universe emerges naturally from critical dynamics of a canonical scalar field coupled to General Relativity. Adopting an inverse power-law potential V(φ) = V₀φ−β (β > 0), the scalar field evolves toward a finite-time critical point t* at which the effective energy density diverges. This divergence marks the breakdown of the effective field description rather than a physical singularity. The continuation of the dynamics beyond t* is non-unique due to the loss of Lipschitz continuity of the equations of motion, established rigorously via the Picard–Lindelöf theorem. This non-uniqueness generates a discrete stratification of the solution space — a countable family of admissible post-critical branches. Compactified logarithmic variables endow the phase space with an effective toroidal topology S¹ × S¹, supporting cyclic and quasi-periodic behavior. The central analytical result is a rigorous derivation of the log-periodic oscillation amplitude and frequency from Floquet analysis of the perturbation equation around the dominant branch, yielding ε ≈ 4.4 × 10⁻³ and ω ≈ 5.2 for the best-fit parameters. These oscillations appear simultaneously in the primordial power spectrum P(k), the CMB angular power spectrum C_ℓ, the Hubble expansion rate H(z), and the matter power spectrum — constituting a coherent, multi-observable signature absent in standard quintessence models. A statistical analysis on 32 cosmic chronometer measurements, BAO (DESI DR1), and Pantheon+ supernovae yields best-fit parameters γ = 0.11 ± 0.04, Ω_φ = 0.57 ± 0.03, H₀ = 68.3 ± 0.9 km/s/Mpc, with ΔAIC = −0.4 over ΛCDM. The framework is sharply falsifiable: non-detection of log-periodic signatures in H(z), C_ℓ, and P(k) by DESI Year-5, CMB-S4, and Euclid would rule it out at > 3σ. Changes in v5: corrected Zenodo DOIs and bibliography titles; Floquet amplitude corrected (C₀/A = 0.01); sections 7–12 unified; γ = 0.11 disambiguated from γ_eff = 1.661; added note on H₀ = 68.3 vs 72.4 km/s/Mpc.