Chaotic hybrid new inflation in supergravity with a running spectral index

We propose an inflation model in supergravity, in which chaotic and hybrid inflation occurs successively, followed by new inflation. During hybrid inflation, adiabatic fluctuations with a running spectral index with $n_s>1\mathrm{}$ on a large scale and $n_s<1\mathrm{}$ on a smaller scale are generated, as favored by recent results of the first year Wilkinson Microwave Anisotropy Probe. The initial condition of new inflation is also set dynamically during hybrid inflation, and its duration and the amplitude of density fluctuations take appropriate values to help early star formation to realize early reionization.