The cosmological action in redshift space

In the standard formulation of cosmological action, the final-time boundary conditions are taken to be the three position coordinates of each galaxy at z = 0. It can be shown that a partial canonical transformation of the action recasts the problem in a coordinate system in which the natural boundary conditions at z = 0 are the angular positions and redshifts relative to a reference galaxy that may itself be in motion. Successful reconstruction of particle orbits back in time, as well as the correct prediction of cosmological parameters, are demonstrated for small systems of particles through conventional N-body simulations.