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 $V(\varphi )=V_0(1+\frac{{\eta }_c}{2}\frac{(\varphi -{\varphi }_c{)}^2}{M_p^2})$, where ${\eta }_c$ is a constant. A natural mechanism to end inflation at $\varphi ={\varphi }_c$ is hybrid type inflation.

18 pages, 7 figures; refs added, version for publication in PRD

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• Measuring the spectral running from cosmic microwave background and primordial black holes
• Constraints on single-field inflation with WMAP, SPT and ACT data -- A last-minute stand before Planck
• Pitfalls of a power-law parameterization of the primordial power spectrum for Primordial Black Hole formation