Viability of slow-roll inflation in light of the non-zero k_min measured
  in the CMB power spectrum
  Slow-roll inflation may simultaneously solve the horizon problem and generate
a near scale-free fluctuation spectrum P(k). These two processes are intimately
connected via the initiation and duration of the inflationary phase. But a
recent study based on the latest Planck release suggests that P(k) has a hard
cutoff, k_min > 0, inconsistent with this conventional picture. Here we
demonstrate quantitatively that most---perhaps all---slow-roll inflationary
models fail to accommodate this minimum cutoff. We show that the small
parameter `epsilon' must be > 0.9 throughout the inflationary period to comply
with the data, seriously violating the slow-roll approximation. Models with
such an epsilon predict extremely red spectral indices, at odds with the
measured value. We also consider extensions to the basic picture (suggested by
several earlier workers) by adding a kinetic-dominated or radiation-dominated
phase preceding the slow-roll expansion. Our approach differs from previously
published treatments principally because we require these modifications
to---not only fit the measured fluctuation spectrum, but to simultaneously
also---fix the horizon problem. We show, however, that even such measures
preclude a joint resolution of the horizon problem and the missing correlations
at large angles.
