Nonnegative Ricci curvature, metric cones and virtual abelianness

Let M be an open n-manifold with nonnegative Ricci curvature.We prove that if its escape rate is not 1/2 and its Riemannian universal cover is conic at infinity, that is, every asymptotic cone (Y, y) of the universal cover is a metric cone with vertex y, then π 1 (M ) contains an abelian subgroup of finite index.If in addition the universal cover has Euclidean volume growth of constant at least L, we can further bound the index by a constant C(n, L).