Cosmological Dynamics and Perturbations from Grand Consistency Theory Background Evolution, Primordial Fluctuations, CMB Transfer, and Structure Growth

This paper develops the cosmological dynamics and perturbation sector of Grand Consistency Theory (GCT), extending its infrared coherence-gravity framework to the evolution and observable structure of the Universe. The cosmological background is governed by the emergent metric, the coherence field C, the effective Planck-mass function M_*²(C), the kinetic response Z_C(C), and the infrared potential U_C(C). The framework describes a continuous cosmological history encompassing primordial accelerated expansion, reheating and thermal evolution, radiation domination, matter domination, and late-time cosmic acceleration. Linear scalar and tensor perturbations are developed to determine the effective gravitational coupling, gravitational slip, lensing response, running Planck mass, propagation speeds, primordial scalar and tensor spectra, and stability conditions. The analysis connects the underlying coherence dynamics with observable quantities including cosmic microwave background anisotropies, acoustic scales, integrated Sachs-Wolfe effects, gravitational lensing, matter growth, and the matter power spectrum. The cosmological response is organized through a compact set of functions governed by the running Planck mass, coherence coupling, effective scalar mass, and propagation speed. The resulting framework provides correlated predictions across background expansion, primordial fluctuations, CMB observables, large-scale structure, weak lensing, and gravitational-wave propagation. These sectors are linked through a common microscopic parameter structure, providing a unified basis for confronting Grand Consistency Theory with cosmological observations.