Nonminimal Coleman-Weinberg inflation with an R² term

We extend the Coleman-Weinberg inflationary model where a scalar field $\varphi$ is non-minimally coupled to gravity with the addition of the R² term. We express the theory in terms of two scalar fields and going to the Einstein frame we employ the Gildener-Weinberg formalism, compute the one-loop effective potential and essentially reduce the problem to the case of single-field inflation. It turns out that there is only one free parameter, namely, the mixing angle between the scalars. For a wide range of this angle, we compute the inflationary observables which are in agreement with the latest experimental bounds. The effect of the R² term is that it lowers the value of the tensor-to-scalar ratio r.