Cosmological Constant from Equivalent Transformation in Quantum Cosmology

We explore the introduction of the cosmological constant via equivalent transformations in cosmology. We consider the Wheeler-DeWitt equation for the CDM universe and we construct the Hamilton-Jacobi action for the $\mathrm{\Lambda }$CDM model. We discuss how this approach allows us to relate different physical systems, providing insights into the role of the cosmological constant in cosmology.