Simple Realization of the Inflationary Expansion of the Universe

The time evolution of the N-vector model coupled to the Einstein field equation in a Robertson-Walker metric is studied numerically under the assumption of initial equilibrium at high temperatures and in the limit as N. The system shows inflationary expansion of the Robertson-Walker scale factor, a (t), over many e-foldings as well as local ordering. The associated structure factor develops a Bragg peak near zero wave number which has the proper weight for a spontaneously broken symmetry and has a width (inversely proportional to a characteristic domain size) which is inversely proportional to a (t).