  The Palatini formulation of the Starobinsky model does not yield a
propagating scalaron that can assume the role of the inflaton field as in the
conventional metric formulation. In the so-called Palatini-${R}^2$ models this
role is assumed by a fundamental scalar field nonminimally coupled to gravity.
In this article we consider an extension of the interactions of this field by
introducing a field dependence to the $R^2$ coefficient in the form of
logarithmic corrections. We examine the resulting predictions of the
inflationary observables in the framework of slow-roll approximation and
investigate the possible implications of the reheating process on these
predictions. We find that the model predictions lie in the favoured region of
the observations and that the assumed scalar field dependence of the $R^2$
coupling tends to decrease the value of the spectral index $n_s$ and
potentially enhance the tensor-to-scalar ratio $r$, circumventing the highly
suppressed values commonly cited for models considered in the same framework.

General Relativity and Quantum Cosmology;High Energy Physics - Theory