Conserved quantities in cosmology

Lake (PRL, 94, 201102, 2005) pointed out that a certain combination (dubbed α) of the density parameter Ω and the cosmological constant 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 spatially closed 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 dust in the cosmological sense) of the universe. Here, I don't dwell on the flatness problem but rather investigate other quantities which correspond to α and other constants of motion in the λ–Ω plane.