SUGRA New Inflation with Heisenberg Symmetry

We propose a realisation of 'new inflation' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the K"ahler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n_s can be close to the best-fit value of the latest Planck 2013 results.