Quantum Entanglement Origin of Gravitational Dynamics

Quantum Entanglement Origin of Gravitational Dynamics: The Θ-Field Theory (Opus 4.5) This preprint proposes a scalar–tensor completion of General Relativity in which spacetime curvature emerges from coarse-grained quantum entanglement. Defining an informational scalar field Θ(x) from the UV-finite mutual information across causal diamonds, we: derive the universal curvature coupling c1=1/(120π)c_{1}=1/(120\pi)c1=1/(120π); obtain a chameleon-screened cosmology consistent with Planck, BAO, and KiDS data; generate an α-attractor plateau potential directly via replica-RG arguments; present hairy black-hole solutions (primary scalar charge QϕQ_\phiQϕ) and show horizon curvature remains finite; predict a ring-down frequency shift δf/f=−λ2Qϕ2/(MPl2M2)\delta f/f=-\lambda^{2}Q_\phi^{2}/(M_{\rm Pl}^{2}M^{2})δf/f=−λ2Qϕ2/(MPl2M2), resolvable by LISA at the 10−510^{-5}10−5 level; demonstrate linear stability and give the one-loop running β(λ)=λ3/(8π2)\beta(\lambda)=\lambda^{3}/(8\pi^{2})β(λ)=λ3/(8π2); provide a Fisher forecast combining LISA ring-down sensitivity with cosmological priors, yielding σ(λ)≃1.5×10−4\sigma(\lambda)\simeq1.5\times10^{-4}σ(λ)≃1.5×10−4.