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

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