Cosmological Predictions of Asymptotic Density Saturation. Paper II: Bounce, Inflation, and Dark Sector Phenomenology from an Effective Theory of Geometric Saturation

I develop the cosmological predictions of an effective theory of asymptotic density saturation (FTAR), consistent with higher-curvature corrections to Einstein gravity expected from quantum effects. A dynamically generated saturation density ρsat arising from conformal-trace-anomaly-induced renormalization group (RG) flow provides a mechanism for singularity avoidance within the effective description and governs the large-scale evolution of the Universe.

Starting from the one-loop effective action for the conformal mode of the metric, I derive: (i) a nonsingular cosmological bounce replacing the Big Bang singularity; (ii) a phase of hilltop-type quasi-de Sitter inflation driven by saturation dynamics without an additional inflaton field; (iii) a primordial perturbation spectrum with spectral index ns≈1−2/N≈0.964 (slow-roll estimate); (iv) a suppression of primordial power at the largest angular scales from the finite bounce duration; (v) reheating from geometric relaxation via universal trace coupling; (vi) a mechanism for stable Planck-mass remnant dark matter; and (vii) an estimate of the residual vacuum energy from incomplete RG relaxation.

Numerical integration of the full FTAR field equations yields a tensor-to-scalar ratio r=1.89×10−4, confirming the strongly hilltop character of the inflationary phase. The Einstein-frame scalar-tensor formulation is shown to be mathematically equivalent to a Jordan-frame f(R) geometric interpretation, linking the saturation mechanism to R2Starobinsky-like gravity at intermediate curvatures.