On Variational Dynamics in Redshift Space

In 1989, Peebles showed that in the gravitational instability picture galaxy orbits can be traced back in time from a knowledge of their current positions, via a variational principle. We modify this variational principle so that galaxy redshifts can be input instead of distances, thereby recovering the distances. As a test problem, we apply the new method to a Local Group model. We infer M = (4–8) × 10 12 M ☉ depending on cosmology, implying that the dynamics of the outlying Local Group dwarfs are consistent with the timing argument. Some algorithmic issues need to be addressed before the method can be applied to recover nonlinear evolution from large redshift surveys, but there are no more difficulties in principle.