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 c urrent-epoch velocity held from the current-epoch density field, or vi ce versa. The scheme implements the idea of Giavalisco et al. that the principle of least action should be used to formulate gravitational i nstability as a two-point boundary-value problem. We argue that the Eu lerian formulation of the problem is to be preferred to the Lagrangian one, on grounds of computational simplicity, of ease of interfacing w ith observational data, and of internal consistency at early times. Th e scheme is successfully tested on an exact solution in one dimension, and on currently Gaussian fields in one and two dimensions. The appli cation of the scheme to real observational data appears to be eminentl y feasible, though computationally costly.