General Relativity as an EFT with emergent gravity via principle of spatial energy potentiality: implications for the standard model of cosmology (2502.18524v3)

Abstract: Recent developments demonstrate that General Relativity (GR) is an effective field theory (EFT) with limited domain of validity, undergoing breakdown of fundamental symmetry in strong fields and exhibiting only one-loop finiteness in perturbative expansion. In this paper, we introduce the Principle of Spatial Energy Potentiality and develop a comprehensive theoretical framework wherein both time and gravity emerge from purely spatial, high-energy configurations through quantum-induced phase transitions. This framework reinterprets the Big Bang as a phase transition from 3D space to 4D spacetime, thereby avoiding traditional singularities and providing alternative early-universe dynamics. We present rigorous mathematical derivations including explicit loop calculations demonstrating how auxiliary parameters become physical time, detailed phase transition dynamics with bubble nucleation analysis, and comprehensive parameter space exploration with realistic energy scales. Modern dimensional regularization techniques reveal the mathematical structure underlying the 3D$\rightarrow$4D transition, showing how power-law divergences transform into logarithmic structures characteristic of emergent spacetime. We develop a thermodynamic analysis demonstrating how Gibbs free energy evolves from a purely enthalpic form in the spatial phase to include entropic contributions as the time arrow emerges. Our approach yields specific testable consequences including cosmic microwave background non-Gaussianities ($f_{NL} \sim 10-50$), gravitational wave backgrounds ($\Omega_{GW} h^2 \sim 10^{-8}-10^{-6}$), and Lorentz invariance violations ($\xi \sim 10^{-3}$), establishing multiple experimental validation pathways. We demonstrate explicit singularity resolution through finite curvature scalars and provide complete mathematical foundation for emergent spacetime dynamics.