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

This preprint presents 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 of this version is a rigorous derivation of the log-periodic oscillation amplitude and frequency from Floquet analysis of the perturbation equation around the dominant post-critical branch. For the best-fit parameters (λ = 0.3, α = 0.45, β = 4), we obtain an oscillation amplitude ε ≈ 4.4 × 10⁻³ and log-frequency ω ≈ 5.2. These signatures appear simultaneously and coherently in the primordial power spectrum P(k), the CMB angular power spectrum Cℓ, the Hubble expansion rate H(z), and the matter power spectrum — constituting a multi-observable smoking-gun signature absent in all standard quintessence models. A statistical analysis performed on 32 cosmic chronometer measurements (Moresco et al. 2022, Borghi et al. 2022, Jiao et al. 2023), BAO data from DESI DR1, and the Pantheon+ supernova compilation yields best-fit parameters γ = 0.11 ± 0.04, Ωφ = 0.57 ± 0.03, H₀ = 68.3 ± 0.9 km s⁻¹ Mpc⁻¹, with ΔAIC = −0.4 over ΛCDM. An entropy-leakage mechanism through black-hole horizons provides a partial dynamical contribution to the Hubble tension (H₀ˡᵒᶜᵃˡ ≈ 69.1 km s⁻¹ Mpc⁻¹). Version 3 introduces four substantive improvements over v2. First, a complete analytical derivation of the log-periodic oscillation amplitude ε and log-frequency ω via Floquet analysis of the linearized perturbation equation around the dominant branch, replacing the qualitative description of previous versions. Second, a quantitative observational plot of H(z) with 32 cosmic chronometer data points, the Stratoverso best-fit curve with 1σ uncertainty band, and the ΛCDM prediction for direct visual comparison. Third, an expanded falsifiability section with six specific quantitative predictions — including numerical amplitudes, log-frequencies, target surveys, and detection timescales (DESI Year-5, Euclid, CMB-S4, LiteBIRD, 2027–2033). Fourth, a discussion of the Stratoverso Framework in relation to recent exponential quintessence analyses (Sultana & Chattopadhyay 2026), demonstrating that the two frameworks are statistically comparable but observationally distinguishable through the log-periodic signatures unique to the Stratoverso. The framework is sharply falsifiable: non-detection of log-periodic signatures in H(z), Cℓ, and P(k) by the next generation of surveys would rule it out at > 3σ. This preprint represents the most complete and quantitative formulation of the Stratoverso Framework to date.