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 $N\to \infty$. The system shows inflationary expansion of the Robertson-Walker scale factor, $a\left(t\right)\mathrm{}$, 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 $a\left(t\right)\mathrm{}$.

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