  The recent measurements of cosmological parameters by the Planck
collaboration favors inflationary models with a redshifted spectrum and a very
low tensor-to-scalar ratio. Two well-studied scenarios in the particle
physics/string theory literature -- inflection point and Starobinsky inflation
-- are in good agreement with these data. In these proceedings, we report on
general studies of these two scenarios. We discuss similarities in their
structure which, we argue, arise from a common mechanism: degenerate critical
point of the potential. In particular, we emphasize their ability to support a
possible primordial explanation for the anomalous suppression of the power
spectrum at large scales.
