Topological Cosmology and Astrophysics: A Complete Global-Realist Theory of Cosmic Evolution, Structure, and Compact Objects from Topological Matter and Historical Disturbance Fields

Abstract

We reconstruct cosmology and astrophysics as the large-scale completion of global realism. The theory begins with one physical substrate, finite topological matter excitations, complete retarded propagation, and the historical disturbance field established in the preceding eleven manuscripts. Dark matter, dark energy, inflationary matter, singular point sources, and homogeneous cosmic geometry are not admitted as independent ontological truths. Each is replaced by, or reduced to, a declared mathematical branch of the common substrate dynamics and is retained only when selected by raw observations. Apparent dark matter is reconstructed as structure-attached collective curvature sourced by organized baryonic history; apparent dark energy is reconstructed through vacuum relaxation, inhomogeneous backreaction, optical propagation, and calibration closure. Both sectors obey causal source, transport, memory, exchange, and decay equations and must reproduce dynamics, lensing, structure growth, and expansion data with one universal parameter dictionary. The so-called Hubble constant is not fundamental in this construction: the primitive quantity is a congruence-dependent local expansion scalar, while \(H_0\) is only the present-epoch value returned after domain averaging, light-cone propagation, source modeling, and calibration. We formulate a many-sorted first-order language, an exhaustive assumption ledger, an axiomatic derivation of the retained gravitational and topological actions, a doubled-field causal influence functional, and a strict derivability certificate separating theorem, definition, boundary datum, controlled closure, and empirical proposition. We derive the covariant master equations, hyperbolic memory dynamics, exact retarded fixed-point representation, constraint propagation, and local well-posedness. From these foundations we construct observation-first light-cone cosmography, inhomogeneous averaging, conditional FLRW dynamics, gauge-invariant perturbations, structure formation, collective curvature, stellar structure and populations, planetary systems, compact objects, nuclear astrophysics, galaxies and clusters, interstellar and intergalactic media, plasma and high-energy processes, lensing, CMB observables, gravitational waves, and multi-messenger inference. Each sector is connected to detector records through an explicit forward map and to parameter reconstruction through an identifiable inverse problem. The resulting work is not an interpretation placed beside conventional cosmology. It is a replacement architecture for the full discipline. Its logical closure does not imply that the required multiscale calculations are small: direct evaluation from topological particle cores to cosmic surveys is computationally enormous. We therefore prove that the actions, kernels, effective fields, and observable equations are derivable at the declared order, provide controlled numerical realizations and error obligations, and leave exhaustive computation and independent empirical testing to the scientific program opened by this theory. The final criterion is uncompromising: where a symmetry branch, collective-curvature kernel, vacuum-relaxation law, or universal parameter set fails independent data, that branch is rejected. Cosmology and astrophysics are thereby re-established as one causal, topological, mathematically closed, and directly falsifiable physical science. **Keywords** Global realism; topological cosmology; topological astrophysics; historical disturbance field; quantum gravity; cosmic evolution; structure formation; collective curvature; vacuum relaxation; dark matter; dark energy; compact objects; gravitational lensing; gravitational waves.