A simple $F(\mathcal{R},\varphi )$ deformation of Starobinsky inflationary model

We study a model including a real scalar field $\varphi$ non-minimally coupled to $F(\mathcal{R})$ gravity, which is conformally equivalent to an Einstein-Hilbert theory, involving two real scalar fields. We consider three special cases of the potential of the field $\varphi$ in the $F(\mathcal{R})$-frame: a vanishing potential, a mass term and a Higgs potential. All these lead to non-trivial two-field potentials in the Einstein-frame which in particular directions resemble the well-known Starobinsky model. We find, that all these cases can yield viable inflationary models in complete agreement with current observational data.