Structure Formation in Unified Quantum Gravity: From Primordial Fluctuations to the Tension

Here, we present a comprehensive analysis of structure formation in Unified Quantum Gravity (UQG), from primordial fluctuations generated during inflation to the formation of galaxies, clusters, and superclusters. The quantum rigidity field $\Pi(x)$ with $N \approx 43$ holographic degrees of freedom modifies structure growth through two mechanisms: (1) scale-dependent corrections to the transfer function $T(k)$ that suppress small-scale power by $\sim 2\%$ at $k > 0.1$ Mpc$^{-1}$, and (2) \textit{quantum friction} that suppresses late-time growth when dark energy dominates. We compute the matter power spectrum $P(k,z)$ and compare with observations from SDSS, DES, and Planck, finding excellent agreement at all observable scales. The effective gravitational constant becomes $G_{\text{eff}}(z) = G_N \times [1 - \eta_\Pi \times \Omega_\Pi(z)]$ where $\eta_\Pi = 0.200$ is the quantum friction parameter, resolving the long-standing $\sigma_8$ tension: UQG predicts $\sigma_8 = 0.797$ at $z=0$ (vs $0.766 \pm 0.020$ from weak lensing) while preserving $\sigma_8 = 0.811$ at recombination (Planck CMB). This is not a phenomenological fit but emerges from spacetime's holographic structure—forming structures costs energy against the vacuum's quantum rigidity. We provide testable predictions for Euclid, LSST, and SKA through growth rate evolution, cluster abundance, and scale-dependent effects.