Inflation with a running spectral index in supergravity

The first year Wilkinson Microwave Anisotropy Probe data favor primordial adiabatic fluctuation with a running spectral index with $n_s>1\mathrm{}$ on a large scale and $n_s<1\mathrm{}$ on a smaller scale. The model building of inflation that predicts perturbations with such a spectrum is a challenge, because most models predict fluctuations with either $n_s>1\mathrm{}$ (hybrid inflation) or $n_s<1\mathrm{}$ (new, chaotic, or topological inflation). We give a sensible particle physics model in supergravity that accommodates the desired running of the spectral index using double inflation.