The_Sigma_Schmidt_Friedmann_Extension__A_Closed_Form_Viscous_Dark_Energy_Model_Beyond_ΛCDM

This work introduces the Sigma–Schmidt Friedmann Extension, a closed-form analytical modification of the standard flat ΛCDM Friedmann equation. The model originates from the Sigma–Schmidt Duality (SSD) framework and describes dark energy as an effective viscous fluid with a transient phantom-like equation of state. The evolution of the dark-energy sector is given by an analytic function Fσ(z)F_\sigma(z)Fσ(z) involving the exponential integral E1(x)E_1(x)E1(x), ensuring numerical stability and early-universe compatibility. The model contains the same cosmological degrees of freedom as flat ΛCDM, with a single additional viscosity parameter ν\nuν. Using publicly available DESI DR2 BAO data (19 measurements), the SSD Friedmann Extension is independently evaluated and compared against ΛCDM. The analysis yields a modest improvement of Δχ2=−1.24\Delta\chi^2 = -1.24Δχ2=−1.24, while AIC/BIC mildly favour ΛCDM due to the one additional parameter. This behaviour is typical of conservative dynamical dark-energy extensions. The model remains fully analytic, stable for all redshifts, and free from Big-Rip divergences. It provides a mathematically controlled and empirically testable framework for studying viscous or dynamical dark energy beyond ΛCDM.