Einstein-Yang-Mills-Maxwell-Inflaton System: I. Initial Value Problem

The general hamiltonian formalism for time-dependent EinsteinYang-Mills equations is presented and then applied to the well studied case of spherically symmetric su(2)−valued Yang-Mills fields. Here, we focus on by far less known time dependent solutions of these equations, and especially on perturbations of Friedmann-Lemaitre homogeneous solutions. By analysing the hamiltonian constraints, we present numerical evidences that the non abelian Yang-Mills fields are more sensitive to inhomogeneity (at least in the expansion rate) than their scalar (inflaton) and abelian (Maxwell) counterparts. Interesting consequences on the process of gravitational instability are briefly outlined here and will be developped in a forthcoming paper.