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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 Omegam is high. It causes an overestimate of the forces and thus an underestimate of Omegam. 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. bullet The solution to the mixed-boundary problem may be non-unique. bullet The method treats the Local Group as an isolated system and neglects possible tidal effects from external material.

Current Results: Peebles [30] obtains ~ 0.15, under the assumption that galaxies strictly trace mass. However, it has been shown using N-body simulations [31] that the assumption that the mass is all in galaxies causes an underestimate of Omegam by a factor 4 - 5 for any true Omegam in the range 0.2 - 1.0. Shaya et al. [32] obtain a similarly low value using a similar analysis inside a sphere of radius ~ 30 h-1Mpc.