Slow-roll reconstruction for running spectral index

Abstract

We not only reconstruct the slow-roll parameters for fit to the running spectral index from WMAP three-year data in the usual slow-roll inflation model and noncommutative inflation model, but also investigate the evolution of these slow-roll parameters. Requiring slow-roll inflation lasts more than 20 e-folds after CMB scales leave the horizon suggests that the potential at the last stage of inflation takes the form $V(\phi)=V_0(1+{\eta_c\over 2}{(\phi-\phi_c)^2\over M_p^2})$, where $\eta_c$ is a constant. A natural mechanism to end inflation at $\phi=\phi_c$ is hybrid type inflation.