Multi-field effects in a simple extension of $R^2$ inflation
  We consider inflation in the system containing a Ricci scalar squared term
and a canonical scalar field with quadratic mass term. In the Einstein frame
this model takes the form of a two-field inflation model with a curved field
space, and under the slow-roll approximation contains four free parameters
corresponding to the masses of the two fields and their initial positions. We
investigate how the inflationary dynamics and predictions for the primordial
curvature perturbation depend on these four parameters. Our analysis is based
on the $\delta N$ formalism, which allows us to determine predictions for the
non-Gaussianity of the curvature perturbation as well as for quantities
relating to its power spectrum. Depending on the choice of parameters, we find
predictions that range from those of $R^2$ inflation to those of quadratic
chaotic inflation, with the non-Gaussianity of the curvature perturbation
always remaining small. Using our results we are able to put constraints on the
masses of the two fields.
