  The lack of large-angle correlations in the fluctuations of the cosmic
microwave background (CMB) conflicts with predictions of slow-roll inflation.
But though probabilities (< 0.24%) for the missing correlations disfavor the
conventional picture at > 3 sigma, factors not associated with the model itself
may be contributing to the tension. Here we aim to show that the absence of
large-angle correlations is best explained with the introduction of a non-zero
minimum wavenumber k_min for the fluctuation power spectrum P(k). We assume
that quantum fluctuations were generated in the early Universe with a
well-defined power spectrum P(k), though with a cutoff k_min not equal to 0. We
then re-calculate the angular correlation function of the CMB and compare it
with Planck observations. The Planck 2013 data rule out a zero k_min at a
confidence level exceeding 8 sigma. Whereas purely slow-roll inflation would
have stretched all fluctuations beyond the horizon, producing a P(k) with
k_min=0---and therefore strong correlations at all angles---a k_min > 0 would
signal the presence of a maximum wavelength at the time (t_dec) of decoupling.
This argues against the basic inflationary paradigm---perhaps even suggesting
non-inflationary alternatives---for the origin and growth of perturbations in
the early Universe. In at least one competing cosmology, the R_h=ct universe,
the inferred k_min corresponds to the gravitational radius at t_dec.
