ACH Cosmological Model: Geometric Extension of ΛCDM with Growth Sector Analysis

This work presents the ACH cosmological model as a phenomenological geometric extension of the standard ΛCDM framework. The model introduces an additional structural term in the Einstein equations: G_{μν} + Θ_{μν} = 8πG T_{μν} Using MCMC reconstruction, the model is tested against cosmological observables. Main result:sigma8 ≈ 0.61 The ACH model remains close to ΛCDM in the background expansion but shows relevant deviations in the growth of structures, suggesting a smooth geometric correction rather than a radical modification of the standard model.