Complete WMAP Constraints on Bandlimited Inflationary Features
  Using a principal component (PC) 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 non-zero 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 PC parameters only improves 2DeltalnL
by 17 for the 20 parameters associated with known glitches in the WMAP power
spectrum at multipoles l<60. We make model-independent predictions for the
matching glitches in the polarization spectrum that would test their
inflationary origin. This complete analysis for bandlimited 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 step-like feature in the potential proposed to
explain the glitch at 20<l<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.
