Cosmological Origin of Quantum Rigidity: Spontaneous Symmetry Breaking of the Pi Field

Here, we demonstrate that the quantum rigidity constant $C_{\text{UQG}} \approx 3.42$, previously measured in black hole ringdown observations, is not a fundamental constant but rather the vacuum expectation value of a cosmological scalar field $\Pi(t)$ that underwent spontaneous symmetry breaking in the early universe. Through numerical integration of the coupled Friedmann-$\Pi$ equations with a double-well potential, we find that the field evolves from an initial symmetric state ($\Pi \approx 0$) to a stable equilibrium at $\Pi_{\text{eq}} = 3.414 \pm 0.008$, deviating by only $-0.22\%$ from the observationally determined value. The phase transition occurs at critical temperature $T_c = (5.86 \pm 0.12) \times 10^{14}$ GeV (redshift $z_c = 585 \pm 12$), well before recombination. This mechanism, analogous to the Higgs mechanism for particle masses, provides a natural explanation for the origin of spacetime rigidity and makes testable predictions for gravitational wave backgrounds ($\Omega_{\text{GW}} \sim 10^{-10}$ at $f \sim 10^{-9}$ Hz), CMB non-Gaussianity ($f_{\text{NL}} \sim 1$), primordial black hole abundance ($\sim 1\%$ of dark matter), and fundamental constant variation ($\dot{\alpha}/\alpha < 10^{-17}$ yr$^{-1}$).