A Candidate Dark Matter Density Evolution Law and Its Implications for Galactic Structure Formation

This preprint proposes a novel dark matter density evolution law ρ_dm(t, S, a) = k ⋅ √(S^(2/3) ⋅ t) / a^(1/4), linking cosmic time, baryonic entropy density, and scale factor. Analytical modeling of Milky Way-like halos shows the law produces cored profiles and flat rotation curves, resolving the cusp-core problem without additional mechanisms. Comparison with NFW and Burkert profiles shows lower RMSE (~3 km/s vs ~11.5 km/s). Includes Python simulation code and visualizations.