  We calculate the covariant one-loop quantum gravitational effective action
for a scalar field model inspired by the recently proposed nonminimal natural
inflation model. Our calculation is perturbative, in the sense that the
effective action is evaluated in orders of background field, around a Minkowski
background. The effective potential has been evaluated taking into account the
finite corrections. An order-of-magnitude estimate of the one-loop corrections
reveals that gravitational and non-gravitational corrections have same or
comparable magnitudes.
