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 may be 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 ΛCDM 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 ~40× faster WMAP7 likelihood method which we have made publicly available.