  We prove a so called $\kappa$ non-inflating property for Ricci flow, which
provides an upper bound for volume ratio of geodesic balls over Euclidean ones,
under an upper bound for scalar curvature. This result can be regarded as the
opposite statement of Perelman's $\kappa$ non-collapsing property for Ricci
flow. These two results together imply volume doubling property for Ricci flow
without assuming Ricci curvature lower bound.
