Natural Double Inflation in Supergravity

We propose a natural double inflation model in supergravity. In this model, chaotic inflation first takes place by virtue of the Nambu-Goldstone-like shift symmetry, which guarantees the absence of the exponential factor in the potential for the inflaton field. During chaotic inflation, an initial value of the second inflation (new inflation) is set. In this model, the initial value of new inflation can be adequately far from the local maximum of the potential for new inflation due to the small linear term of the inflaton in the K\"ahler potential. Therefore, the primordial fluctuations within the present horizon scale may be attributed to both inflations; that is, the first chaotic inflation produces the primordial fluctuations on the large cosmological scales while the second new inflation on the smaller scales. The successive decay of the inflaton for new inflation leads to a reheating temperature low enough to avoid the overproduction of gravitinos in a wide range of the gravitino mass.