Yet another variant of the numerical action method is presented and applied to an analysis of the redshifts of galaxies in the range of distances from the Fornax, Leo I, and Leo II dwarf spheriodal companions of the Milky Way to the outer parts of the Local Group. Orbits consistent with observed redshifts follow if the mass concentrated around the Milky Way is about 2 × 1012 Msun and the other nearby galaxies at distances ≲ 3 Mpc have similar mass-to-light ratios. If this is a fair measure of the mass, then the cosmological density parameter is Ω ∼ 0.1. If Ω = 1, then the distribution of the other ∼90% of the mass as a function of distance from the Milky Way in the range 0.3 ≲ r ≲ 3 Mpc has to be close enough to homogeneous that it does not cause unacceptably large relative velocities of the nearby groups. This would be difficult to understand if Ω = 1 and the dominant component of the dark mass had negligibly small pressure, because one would have expected giant galaxies to have accreted massive halos with radii ≳1 Mpc.
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P. J. E. Peebles (1995) studied this question.