Effective Saturation Cosmology: A Minimal Model with Nonsingular Bounce and Inflationary Continuation

This preprint presents a minimal effective cosmological model in which a single saturating scalar closure modifies the high-density regime of flat FLRW evolution. The scalar field potential is V(φ)=ρₛₐₜ/2 ^2(φ/φ_), and the model yields a saturation-modified Friedmann equation of the form H^2 ∝ ρ(1-ρ/ρₛₐₜ). The paper studies two narrowly defined questions: whether the model admits a nonsingular bounce at finite density; whether the same effective closure supports a subsequent slow-roll inflationary continuation. Within the model, the paper derives the modified Friedmann and Raychaudhuri equations, identifies the sign flip of H at ρ=ρₛₐₜ/2, analyzes the local bounce structure, and discusses the status of the defocusing condition. It then studies the post-bounce slow-roll regime and extracts representative scalar and tensor observables. Main result: within this effective background model, the saturation closure supports both bounce regularization and a low-r inflationary hierarchy in a single framework. Scope limitations are explicit. This work does not provide a complete treatment of perturbation transfer through the bounce, reheating, dark matter abundance, late-time vacuum energy, or nonperturbative ultraviolet completion. Quantitative outputs depend on the chosen closure, parameter values, and post-bounce initial conditions and should be read as model-dependent results rather than robust predictions of a complete cosmological theory. Author: Michał Jerzy Drewnisz (Independent Researcher, Warsaw, Poland; ORCID: 0009-0009-6050-5055).