Using Perturbative Least Action to Reconstruct the Local Group

In this paper, we apply the Perturbative Least Action Method to model the Local Group of galaxies for various Cosmological models. We show that though the galaxy masses are theoretically good discriminators of ${\mathrm{\Omega }}_M$ given some observed MW and M31 separation and radial velocity, current estimates of the masses are insufficient to make any cosmological claims. We then discuss additional complications to expand this analysis.