Inflation in a conformally-invariant two-scalar-field theory with an
  extra $R^2$ term
  We explore inflationary cosmology in a theory where there are two scalar
fields which non-minimally couple to the Ricci scalar and an additional $R^2$
term, which breaks the conformal invariance. Particularly, we investigate the
slow-roll inflation in the case of one dynamical scalar field and that of two
dynamical scalar fields. It is explicitly demonstrated that the spectral index
of scalar mode of the density perturbations and the tensor-to-scalar ratio can
be consistent with the observations acquired by the recent Planck satellite.
The graceful exit from the inflationary stage is achieved as in convenient
$R^2$ gravity. We also propose the generalization of the model under discussion
with three scalar fields.
