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Abstract <p>A renormalization-group mechanism for the resolution of spacetime singularities is formulated on the basis of the Relativistic Zero Point (RZP) principle. The quantum vacuum is modeled as a geometric medium described by an order parameter Θ, whose flow is constrained by Functional Renormalization Group (FRG) equations. A scalar-tensor truncation yields a non-Gaussian fixed point (NGFP) with parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\xi \approx 0.65\)</EquationSource> <!--JETP2560177Machi-m1--> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{\lambda }_{*}} \approx 0.42\)</EquationSource> <!--JETP2560177Machi-m2--> </InlineEquation>, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({{\nu }_{*}} \approx 1.00\)</EquationSource> <!--JETP2560177Machi-m3--> </InlineEquation>. The resulting transition <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Theta \to {{\nu }_{*}}\)</EquationSource> <!--JETP2560177Machi-m4--> </InlineEquation> replaces classical divergences with a smooth bounce horizon. The formulation consolidates previous developments [1, 2] and integrates the scalar-tensor RZP construction [3]. Phenomenological predictions include a tensor-to-scalar ratio <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(r \sim 0.025\)</EquationSource> <!--JETP2560177Machi-m5--> </InlineEquation>, a gravitational-wave dispersion scale <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\epsilon \sim 8.3 \times {{10}^{{ - 8}}}\)</EquationSource> <!--JETP2560177Machi-m6--> </InlineEquation>, and expected post-merger echo delays of order <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Delta t \sim 4.2\)</EquationSource> <!--JETP2560177Machi-m7--> </InlineEquation> ms.</p>

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

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Abdul Sahib Machi García

摘要

Abstract

A renormalization-group mechanism for the resolution of spacetime singularities is formulated on the basis of the Relativistic Zero Point (RZP) principle. The quantum vacuum is modeled as a geometric medium described by an order parameter Θ, whose flow is constrained by Functional Renormalization Group (FRG) equations. A scalar-tensor truncation yields a non-Gaussian fixed point (NGFP) with parameters \(\xi \approx 0.65\) , \({{\lambda }_{*}} \approx 0.42\) , and \({{\nu }_{*}} \approx 1.00\) . The resulting transition \(\Theta \to {{\nu }_{*}}\) replaces classical divergences with a smooth bounce horizon. The formulation consolidates previous developments [1, 2] and integrates the scalar-tensor RZP construction [3]. Phenomenological predictions include a tensor-to-scalar ratio \(r \sim 0.025\) , a gravitational-wave dispersion scale \(\epsilon \sim 8.3 \times {{10}^{{ - 8}}}\) , and expected post-merger echo delays of order \(\Delta t \sim 4.2\) ms.