Cosmological Bounce Horizon from First Principles: FRG-derived Resolution of Singularities via Relativistic Zero Point

A renormalization-group mechanism for the resolution of spacetime singularities isformulated on the basis of the Relativistic Zero Point (RZP) principle. The quantumvacuum is modeled as a geometric medium described by an order parameter Θ, whoseflow is constrained by Functional Renormalization Group (FRG) equations. A scalartensortruncation yields a non-Gaussian fixed point (NGFP) with parameters ξ ≈ 0.65,λ∗ ≈ 0.42, and v∗ ≈ 1.00. The resulting transition Θ → v∗ replaces classical divergenceswith a smooth bounce horizon. The formulation consolidates previous developments [1,2] and integrates the scalar-tensor RZP construction [3]. Phenomenological predictionsinclude a tensor-to-scalar ratio r ∼ 0.025, a gravitational-wave dispersion scale ϵ ∼8.3 × 10−8, and expected post-merger echo delays of order Δt ∼ 4.2 ms.