The least action principle (LAP) is a dynamically rigorous method for deriving the history of galaxy orbits. In particular it is an Omega test, predicting current epoch galaxy velocities as a function of position and of the cosmological background. It is most usefully applied to in-falling structures, such as the local group, where its application indicates that the preferred cosmological model is Omega(0) = 0.1 and h = 0.75 (h is the Hubble parameter in units of 100 km s(-1) Mpc(-1)). The method assumes that all the mass acts as if it were distributed as the visible galaxies. We test the reliability of the LAP to Local Group-like systems extracted from Omega(0) = 1 n-body simulations. While the orbits of the galaxies are qualitatively well reconstructed, the LAP systematically underestimates the mass of the system. This failure is attributed to the presence of extended halos weakly clustered around visible galaxies which prevent a large fraction of the group mass from being detected by the LAP technique. We conclude that the LAP method cannot rule out an Omega(0) = 1 value on the Local Group scale. Better constraints on Omega(0) may be obtained by applying this technique to in-falling systems, such as clusters, containing objects with separations large compared to galaxy sizes.
Branchini, E.F., Carlberg, R.g. (1994). TESTING THE LEAST ACTION PRINCIPLE IN AN OMEGA(0)=1 UNIVERSE. THE ASTROPHYSICAL JOURNAL, 434(1), 37-45 [10.1086/174702].