Evidence of a truncated spectrum in the angular correlation function of the cosmic microwave background

Aim. The lack of large-angle correlations in the fluctuations of the cosmic microwave background (CMB) conflicts with predictions of slow-roll inflation. But while probabilities (≲ 0.24%) for the missing correlations disfavour the conventional picture at ζ 3σ, 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 wave number k_min for the fluctuation power spectrum P(k). Methods. We assumed that quantum fluctuations were generated in the early Universe with a well-defined power spectrum P(k), although with a cut-off k_min≠ 0. We then re-calculated the angular correlation function of the CMB and compared it with Planck observations. Results. The Planck 2013 data rule out a zero k_min at a confidence level exceeding 8σ. 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, and perhaps even suggests 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.