New inflation in supergravity after Planck and LHC

We revisit a single-field new inflation model based on a discrete R symmetry. Interestingly, the inflaton dynamics naturally leads to a heavy gravitino of mass m3/2=O(1-100)TeV, which is consistent with the standard-model like Higgs boson of mass m_h≃126GeV. However, the predicted spectral index n_s≈0.94 is in tension with the Planck result, n_s=0.9603±0.073. We show that the spectral index can be increased by allowing a small constant term in the superpotential during inflation. The required size of the constant is close to the largest allowed value for successful inflation, and it may be a result of a pressure toward larger values in the landscape. Alternatively, such constant term may arise in association with supersymmetry breaking required to cancel the negative cosmological constant from the inflaton sector.