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.Comment: 13 pages, to appear in Phys. Rev.
