A Unified Nonsingular Cosmology from a Minimal Effective Density Modification

I present a unified nonsingular cosmological model based on a minimal modification of the effective energy density, where the effective density is given by rho_eff = rho − alpha * rho^2. This modification produces a natural cosmological bounce at high densities without introducing new fields, exotic matter, or violations of standard energy conditions. The model reduces to standard cosmology at low densities while resolving the big‑bang singularity at high densities. I derive the modified Friedmann dynamics, analyze scalar perturbations using the Mukhanov–Sasaki equation, and compute the resulting power spectrum. The framework yields scale‑invariant perturbations through the bounce and predicts observational signatures including modified non‑Gaussianity and characteristic imprints on the matter power spectrum. This minimal effective‑density approach provides a simple, self‑consistent, and observationally testable alternative to inflationary and quantum‑gravity‑based nonsingular cosmologies.