CoreLumen Cosmology I : Condensate Inflation

This work presents the first paper of the CoreLumen Cosmology series. Within the CoreLumen framework the physical vacuum is modeled as aphase condensate described by the complex order parameter Ψ = ρ e^{iθ}. In this picture cosmic expansion is governed by the dynamics of thecondensate background rather than by a separate inflaton field. The present work focuses on the background inflationary regime.We demonstrate that a quasi–de Sitter inflationary phase naturallyemerges when the condensate amplitude evolves in the overdamped regimecharacterized by the parameter Ξ = 3H / m_eff. In this limit the Hubble friction term dominates the condensate dynamics,producing slow evolution of the vacuum energy density and an acceleratedcosmic expansion. This paper establishes the inflationary background solution of theCoreLumen cosmological framework and serves as the starting point forthe subsequent analysis of primordial perturbations and structureformation. Future papers in the series will address perturbation theory,thermal history, matter domination, and late–time cosmic acceleration.