### Abstract

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}.

Original language | English (US) |
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Article number | A87 |

Journal | Astronomy and Astrophysics |

Volume | 610 |

DOIs | |

Publication status | Published - Feb 1 2018 |

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### Keywords

- Cosmic background radiation
- Cosmology: Observations
- Cosmology: Theory
- Early Universe
- Inflation
- Large-scale structure of Universe

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astronomy and Astrophysics*,

*610*, [A87]. https://doi.org/10.1051/0004-6361/201732181