The Principle of Least Action and Clustering in Cosmology

A scheme is developed which enables one to trace backwards in time the cosmic density and velocity fields, and to determine accurately the current-epoch velocity field from the current-epoch density field, or vice versa. The scheme implements the idea of Giavalisco \etal\ (1993) that the principle of least action should be used to formulate gravitational instability as a two-point boundary-value problem. We argue that the Eulerian formulation of the problem is to be preferred to the Lagrangian one, on grounds of computational simplicity, of ease of interfacing with observational data, and of internal consistency at early times. The scheme is successfully tested on an exact solution in one dimension, and on currently Gaussian fields in one and two dimensions. The application of the scheme to real observational data appears to be eminently feasible, though computationally costly.