  We investigate a model of inflationary cosmology where the minimally coupled
scalar field theory is modified by additional correction terms. Among the most
general ten correction terms remarked by Weinberg in context of effective field
theory, we consider only two terms, $f_1(\phi) R^2$ and $f_2(\phi)
R^{ab}R_{ab}$, following the work by Noh and Hwang where $f_1$ and $f_2$ are
constant. The fourth order differential equations for the background universe
and the tensor-type perturbation are derived out of this model. We show that
these equations can be reduced to second order equations, supposing that $f_n$
are small. From these approximated equations, we find that the propagation
speed of gravitational wave is slightly less than the speed of light due to
$f_2$ term, and that the evolution of the tensor-type perturbation is conserved
in the large scale limit.
