The UAT Lagrangian Formulation: Derivation of the Quantum Braking Action, Causal Parameters, and CMB Acoustic Peak Predictions

Description:This repository contains the complete theoretical and mathematical foundation of the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) framework. It transitions the UAT from a phenomenological model resolving the Hubble tension to a rigorous scalar-tensor field theory. The core of this release is the derivation of the UAT Lagrangian, demonstrating that the dynamics of cosmic expansion are governed by a causal scalar field ϕ non-minimally coupled to gravity. Repository Contents: The UAT Lagrangian (Main Paper): Derives the exact values of the non-minimal coupling (ξ=−0.2810) and the vacuum self-coupling (λ=3.08×10 −112 in Planck units). These parameters are not arbitrary but rigidly fixed by the causal limit (κ crit =4.978) and the 7% thermal calibration margin at recombination. Observational Predictions (CMB): Contains the theoretical predictions for the displacement of the CMB acoustic peaks. The UAT framework predicts a structural shift of Δℓ/ℓ=+5.85% and an alteration in the shift parameter R to 1.7750, driven by the modified sound horizon (r d ≈141.00 Mpc). Parameter Derivation Code: The Python script executing the numerical closure of the UAT parameters. Methodological Note for Future Implementation:The analytical closure presented here forms the definitive theoretical groundwork of the UAT. Full dynamic integration and confrontation with high-precision cosmological datasets (like the full Planck likelihoods) exceed the capabilities of standard numerical libraries. A complete validation pipeline will require the explicit integration of this scalar-tensor Lagrangian into advanced Boltzmann Solvers (such as CLASS or CAMB). This repository establishes the exact theoretical metrics and target parameters required for those future modifications."This update (v2) adds the resolution of the effective matter density problem: the identity η ≡ κ_crit and the causal membrane integral explaining why Ω_m^(eff) = Ω_b × 7.49. Includes numerical solution of the Klein-Gordon equation demonstrating field freezing." Author: Miguel Ángel [email protected]