  This is the second article of a sequence of research on deformations of
Q-curvature. In the previous one, we studied local stability and rigidity
phenomena of Q-curvature. In this article, we mainly investigate the volume
comparison with respect to Q-curvature. In particular, we show that volume
comparison theorem holds for metrics close to strictly stable positive Einstein
metrics. This result shows that Q-curvature can still control the volume of
manifolds under certain conditions, which provides a fundamental geometric
characterization of Q-curvature. Applying the same technique, we derive the
local rigidity of strictly stable Ricci-flat manifolds with respect to
Q-curvature, which shows the non-existence of metrics with positive Q-curvature
near the reference metric.
