📝 SummarXiv

Abstract

General Relativity is an effective field theory with limited validity, undergoing breakdown in strong fields and exhibiting only one-loop finiteness. We introduce the Principle of Spatial Energy Potentiality and develop a 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, avoiding traditional singularities. 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 parameter space exploration. Dimensional regularization techniques reveal the mathematical structure underlying the 3D$\rightarrow$4D transition, showing how power-law divergences transform into logarithmic structures characteristic of emergent spacetime. Our approach yields testable consequences including cosmic microwave background non-Gaussianities ($f_{NL} \sim 20-50$), gravitational wave backgrounds ($\Omega_{GW} h^2 \sim 10^{-8} - 10^{-6}$), Lorentz invariance violations ($\xi \sim 10^{-3}$), and controlled Big Bang nucleosynthesis modifications. The framework naturally resolves the Hubble tension through scale-dependent modifications to cosmic expansion, explaining the $\sim$7\% discrepancy between early-universe ($H_0 \approx 67.4$ km/s/Mpc) and late-universe ($H_0 \approx 73.0$ km/s/Mpc) measurements without additional parameters. This work establishes emergent spacetime as a viable framework with broad implications for quantum gravity and cosmology, providing unified models addressing fundamental questions while offering rigorous alternatives to standard cosmological paradigms.