Conserved quantities in cosmology

Lake pointed out that a certain combination (which he dubbed α) of Ω and λ is a constant of motion for evolutionary trajectories in the λ–Ω plane and used mapping between α and the λ–Ω plane to demonstrate the lack of a flatness problem for cosmological models with a positive cosmological constant which will expand forever. In such models, the conserved quantity corresponds to the product of λ and the square of the mass of the universe. I investigate other quantities which correspond to α and other constants of motion in the λ–Ω plane.