Inflationary universe in a conformally-invariant two scalar-field theory
  with an $R^2$ term
  We investigate the inflationary universe in a theory where two scalar fields
non-minimally coupling to the scalar curvature and an extra $R^2$ term exist
and the conformal invariance is broken. In particular, the slow-roll inflation
is explored for the case that one scalar field is dynamical and that two scalar
fields are dynamical. As a result, we show that the spectral index of the
curvature perturbations and the tensor-to-scalar ratio of the density
perturbations can be compatible with the Planck results. It is also
demonstrated that the graceful exit from inflation can be realized.
