Slow-roll reconstruction for running spectral index

Abstract

We reconstruct from the Wilkinson microwave anisotropy probe three-year data the slow-roll parameters in the standard slow-roll inflation model and the noncommutative inflation model. We also investigate the evolution of these slow-roll parameters. Requiring that slow-roll inflation lasts more than 20 e-folds after cosmic microwave background scales leave the horizon, we find that the potential at the last stage of inflation takes the form $V(\ensuremath{\phi})={V}_{0}(1+\frac{{\ensuremath{\eta}}_{c}}{2}\frac{(\ensuremath{\phi}\ensuremath{-}{\ensuremath{\phi}}_{c}{)}^{2}}{{M}_{p}^{2}})$, where ${\ensuremath{\eta}}_{c}$ is a constant. A natural mechanism to end inflation at $\ensuremath{\phi}={\ensuremath{\phi}}_{c}$ is the hybrid-type inflation.