CMB Constraints on Principal Components of the Inflaton Potential
  We place functional constraints on the shape of the inflaton potential from
the cosmic microwave background through a variant of the generalized slow roll
approximation that allows large amplitude, rapidly changing deviations from
scale-free conditions. Employing a principal component decomposition of the
source function G'~3(V'/V)^2 - 2V''/V and keeping only those measured to better
than 10% results in 5 nearly independent Gaussian constraints that maybe used
to test any single-field inflationary model where such deviations are expected.
The first component implies < 3% variations at the 100 Mpc scale. One component
shows a 95% CL preference for deviations around the 300 Mpc scale at the ~10%
level but the global significance is reduced considering the 5 components
examined. This deviation also requires a change in the cold dark matter density
which in a flat LCDM model is disfavored by current supernova and Hubble
constant data and can be tested with future polarization or high multipole
temperature data. Its impact resembles a local running of the tilt from
multipoles 30-800 but is only marginally consistent with a constant running
beyond this range. For this analysis, we have implemented a ~40x faster WMAP7
likelihood method which we have made publicly available.
