Complete WMAP constraints on band-limited inflationary features

Abstract

Using a principal component basis that accommodates order unity features in the slow-roll parameters as fine as $1/10$ of a decade across more than 2 decades of the inflationary expansion, we test slow-roll and single-field inflation with the WMAP7 data. Detection of any nonzero component would represent a violation of ordinary slow roll and indicate a feature in the inflaton potential or sound speed. Although one component shows a deviation at the 98% CL, it cannot be considered statistically significant given the 20 components tested. The maximum likelihood principal component parameters only improve $2\ensuremath{\Delta}\mathrm{ln}L$ by 17 for the 20 parameters associated with known glitches in the WMAP power spectrum at multipoles $\ensuremath{\ell}<60$. We make model-independent predictions for the matching glitches in the polarization spectrum that would test their inflationary origin. This complete analysis for band-limited features in the source function of generalized slow roll can be used to constrain parameters of specific models of the inflaton potential without requiring a separate likelihood analysis for each choice. We illustrate its use by placing bounds on the height and width of a steplike feature in the potential proposed to explain the glitch at $20\ensuremath{\le}\ensuremath{\ell}\ensuremath{\le}40$. Even allowing for the presence of features in the temperature spectrum, single-field inflation makes sharp falsifiable predictions for the acoustic peaks in the polarization whose violation would require extra degrees of freedom.