Higgs Inflation as Nonlinear Sigma Model and Scalaron as its
  $\sigma$-meson
  We point out that a model with scalar fields with a large nonminimal coupling
to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear
sigma model (NLSM). With the inclusion of not only the scalar fields but also
the conformal mode of the metric, our definition of the target space of the
NLSM is invariant under the frame transformation. We show that the
$\sigma$-meson that linearizes this NLSM to be a linear sigma model (LSM)
corresponds to the scalaron, the degree of freedom associated to the $R^2$ term
in the Jordan frame. We demonstrate that quantum corrections inevitably induce
this $\sigma$-meson in the large-$N$ limit, thus providing a frame independent
picture for the emergence of the scalaron. The resultant LSM only involves
renormalizable interactions and hence its perturbative unitarity holds up to
the Planck scale unless it hits a Landau pole, which is in agreement with the
renormalizability of quadratic gravity.
