3.4. Local Group Dynamics
The mixed-boundary problem of a cosmological gravitating system is solved for the trajectories of galaxies in the Local Group. It is done using the least-action principle, under the assumption that the mass is concentrated around the galaxies (i.e., strict no biasing).
New Developments: Simulations are being used to estimate the biases in the method.
Pro: This method is making use of accurate local measurements.
Con: The assumption that the mass is all in point-like galaxies during the whole evolution of the Local Group is likely to be wrong, especially if m is high. It causes an overestimate of the forces and thus an underestimate of m. This is a stronger assumption than assuming no biasing in the statistical sense, b = 1. A related problem is the neglect of possible merging that has taken place among the initial subsystems in the Local Group. The solution to the mixed-boundary problem may be non-unique. The method treats the Local Group as an isolated system and neglects possible tidal effects from external material.
Current Results: Peebles  obtains ~ 0.15, under the assumption that galaxies strictly trace mass. However, it has been shown using N-body simulations  that the assumption that the mass is all in galaxies causes an underestimate of m by a factor 4 - 5 for any true m in the range 0.2 - 1.0. Shaya et al.  obtain a similarly low value using a similar analysis inside a sphere of radius ~ 30 h-1Mpc.