Ricci-flat deformations of metrics with exceptional holonomy

Let G be one of the Ricci-flat holonomy groups SU(n), Sp(n), Spin(7) or G2, and M a compact manifold of dimension 2n, 4n, 8 or 7, respectively. We prove that the natural map from the moduli space of torsion-free G-structures on M to the moduli space of Ricci-flat metrics is open, and that the image is a smooth manifold. For the exceptional cases G = Spin(7) and G2, we extend the result to asymptotically cylindrical manifolds.