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

Abstract

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.