  Theories with curvature squared terms in the action are known to contain
ghost modes in general. However, if we regard curvature squared terms as
quantum corrections to the original theory, the emergence of ghosts may be
simply due to the perturbative truncation of a full non-perturbative theory. If
this is the case, there should be a way to live with ghosts. In this paper, we
take the Euclidean path integral approach, in which ghost degrees of freedom
can be, and are integrated out in the Euclideanized spacetime. We apply this
procedure to Einstein gravity with a Weyl curvature squared correction in the
inflationary background. We find that the amplitude of tensor perturbations is
modified by a term of O(alpha^2 H^2) where alpha^2 is a coupling constant in
front of the Weyl squared term and H is the Hubble parameter during inflation.
