A Minimal Effective Saturation Cosmology with a Nonsingular Bounce and Representative Inflationary Continuation

Status: Preprint submitted for peer review (March 2026). Abstract: We study a minimal effective cosmological model in which a single saturating scalar closure modifies the high-density regime of flat FLRW evolution. The action is Einstein gravity minimally coupled to a scalar field with the potential V(ϕ)=2ρsattanh2(ϕ/ϕ∗), which yields a saturation-modified Friedmann equation of the form H2∝ρ(1−ρ/ρsat). The purpose is limited: to show that the resulting dynamics admit a nonsingular bounce at finite density, with the defocusing condition satisfied at the bounce point, and that the same effective potential supports a subsequent slow-roll inflationary plateau for a suitable parameter range. We derive the modified Friedmann and Raychaudhuri equations, identify the sign flip of H˙ at ρ=ρsat/2, and analyze the local bounce structure. We then analyze the post-bounce slow-roll regime and extract representative scalar and tensor observables. The main conclusion is structural: the saturation closure supports both bounce regularization and a low-r inflationary hierarchy within a single effective background model. Quantitative outputs depend on the chosen closure, parameter values, and initial conditions, and should not be read as robust predictions of a complete cosmological theory. The paper does not address the trans-bounce evolution of specific perturbation modes, full UV-complete quantum gravity embedding, or late-time dark energy.