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We calculate the covariant one-loop quantum gravitational effective actionfor a scalar field model inspired by the recently proposed nonminimal naturalinflation model. Our calculation is perturbative, in the sense that theeffective action is evaluated in orders of background field, around a Minkowskibackground. The effective potential has been evaluated taking into account thefinite corrections. An order-of-magnitude estimate of the one-loop correctionsreveals that gravitational and non-gravitational corrections have same orcomparable magnitudes.

Covariant quantum corrections to a scalar field model inspired by nonminimal natural inflation