The principle of least action and clustering in cosmology

Abstract

A scheme is developed which enables one to trace backwards in time the cosmic density and velocity elds, and to determine accurately the current-epoch velocity eld from the current-epoch density eld, or vice versa. The scheme implements the idea of Giavalisco et al. (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 elds in one and two dimensions. The application of the scheme to real observational data appears to be eminently feasible, though computationally costly.

Reconstruction of cosmological density and velocity fields in the Lagrangian Zel'dovich approximation

“…This principle was used together with the assumption that the initial peculiar velocities of galaxies are zero in order to predict galaxy orbits in the local group (Peebles 1989) and for galaxies within 3000 kms 1 (Shaya, Peebles and Tully 1995). Giavalisco (1993) and Susperregi and Binney (1994) also use least action in the context of an evolving mass distribution, in the latter case applied to mass smoothed onto an Eulerian grid.…”

Anisotropic hubble expansion of large scale structures

“…• if α = 0 then Q has a real double root η 1 = η 2 and a simple one η 3 . The related instantaneous kinematic shows a planar-axial symmetry (either a contraction within a plane with an expansion toward a transverse direction or vice versa), see Sect.…”

“…Later on, least action methods [2] were also used in reconstruction procedures with more reliable estimates, see e.g. [3][4][5][6][7]. Both approaches assume that the peculiar velocity field decomposes into a "divergent" component due to density fluctuations inside the surveyed volume, and a tidal (shear) component, consisting of a bulk velocity and higher moments, due to the matter distribution outside the surveyed volume [8].…”

Reconstruction of the early Universe as a convex optimization problem

“…Cosmological reconstruction should, however, take advantage of our knowledge that the initial mass distribution was quasi‐uniform at baryon–photon decoupling, about 14 billion years ago (see, e.g., Susperregi & Binney 1994). In a recent Letter to Nature (Frisch et al 2002), four of us have shown that, with suitable assumptions, this a priori knowledge of the initial density field makes reconstruction a well‐posed instance of what is called the optimal mass transportation problem.…”