Complex Spacetime: The Origin of the Universe Volume Six: Cosmology & Observational Predictions

Abstract: This paper derives cosmological equations and observable predictions from Pangu Geometry. The real part of complex spacetime gives Einstein gravity (FRW cosmology), while the imaginary part gives dark energy and topological dark matter contributions. Core predictions include: (1) unparticle dark matter density $\Omega_{\mathrm{top}}=0.1188/0.674^2\approx0.261$; (2) dark energy $\Omega_\Lambda\approx0.690$ (the three-fold topological suppression provides the physical direction, but the complete dimensional chain is still short by $\sim$51 orders of magnitude; currently a phenomenological benchmark); (3) scalar polarization mode fraction of gravitational waves $R=\pi^2/2048\approx0.48\%$; (4) CP violation from the complex phase provides a baryogenesis mechanism (see Paper 5). $E_0$ is calibrated from the electroweak scale (with $K_T$ and $\mathcal{C}$ as phenomenological calibration factors), while core predictions such as the polarization ratio have no free parameters and are testable by future observations.