Cosmological Consequences of the $S^5/I^*$ Orbifold Geometry

We derive cosmological consequences of the geometric framework based on the orbifold $S^5/I^*$ with $E_8$ gauge group, building upon the companion paper on fermion masses. The relation $M_P^2 = 248 M_*^2$ ($f_{\mathrm{KK}} \approx 1.0$) and 248 phonon modes yield Starobinsky inflation ($n_s \approx 0.965$, $r \approx 0.0030 \pm 0.0005$). Brane collisions produce a dense cosmic string network ($\mu_{\mathrm{eff}} \sim 10^{30}$ GeV$^2$, $G\mu \sim 7.4 \times 10^{-9}$). A novel mechanism is proposed: the gravitational collapse time of string clusters is comparable to the communication time required for gauge orientation exchange, and $\sim 10^7$ times shorter than the gravitational wave emission time from string oscillations. Consequently, the standard nanohertz background from oscillating strings is never produced. Strings in cluster cores ($f_{\mathrm{collapse}} \sim 0.9$) collapse into primordial black holes ($M_{\mathrm{BH}} \sim 5.9 \times 10^{37}$ GeV, $\sim 1.1 \times 10^{14}$ g), while peripheral strings ($f_{\mathrm{ann}} \sim 0.1$) annihilate and drive reheating ($T_{\mathrm{reh}} \sim 2 \times 10^{15}$ GeV). Gravitational waves from black hole horizon formation produce a stochastic background with a unique double-peak structure: a millihertz peak at $f \sim 9 \times 10^{-6}$ Hz accessible to LISA, and a nanohertz peak at $f \sim 4 \times 10^{-11}$ Hz accessible to pulsar timing arrays. A primordial dark age is predicted between string collapse ($t \sim 10^{-35}$ s) and PBH evaporation ($t \sim 200,000$ yr), during which all information about earlier epochs is erased by thermalisation. The geometry of $S^2/A_5$ predicts two CMB anomalies observed by Planck at $2$--$3\sigma$: the axis of evil (from the normal to the fundamental triangle) and the cold spot (from the conical singularity at $V_2$). Baryon asymmetry ($\eta_B \sim 3.4 \times 10^{-10}$) is generated by geometric Berry phases and frozen in after $E_8$-sphaleron freeze-out ($\kappa = 7/16$). Dark matter, the strong CP problem, the $W$-boson mass anomaly, and dark energy evolution are addressed in the companion paper. Fifteen experimental predictions are summarised in a table spanning 2025--2040+.