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). The $\sigma$-meson, which is induced by quantum corrections, is identified as the scalaron in this model. Our understanding provides a novel alternative picture for the emergence of the scalaron, which was previously studied in the Jordan frame by computing the running of the term quadratic in the Ricci scalar. We demonstrate that quantum corrections inevitably induce other operators on top of this NLSM, which give rise to the $\sigma$-meson. We confirm that the $\sigma$-meson indeed corresponds to the scalaron. With the help of the $\sigma$-meson, the NLSM is UV-completed to be a linear sigma model (LSM). We show that the 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.