Observational constraints on inflation with the nonlinear sigma fields in light of Plank 2015

We study an inflation model with a nonlinear sigma field which has $SO(3)$ symmetry. The background solution of the nonlinear sigma field is proportional to the space coordinates linearly while keeping the homogeneous and isotropic background spacetime. We calculate the observable quantities including the power spectra of the scalar and tensor modes, the spectral indices, the tensor-to-scalar ratio, and the running of the spectral indices, and then constrain our model with the Planck 2015 observational data.