Hint of a truncated primordial spectrum from the CMB large-scale anomalies

¹ Department of Physics, The Applied Math Program, and Department of Astronomy, The University of Arizona, Tucson, AZ 85721, USA
e-mail: fmelia@email.arizona.edu
² Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, and School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550001, PR China
³ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, PR China
⁴ Guangxi Key Laboratory for Relativistic Astrophysics, Guangxi University, Nanning 530004, PR China
⁵ University of Chinese Academy of Sciences, Beijing 100049, PR China

Received: 4 May 2021
Accepted: 12 September 2021

Abstract

Context. Several satellite missions have uncovered a series of potential anomalies in the fluctuation spectrum of the cosmic microwave background temperature, including: (1) an unexpectedly low level of correlation at large angles, manifested via the angular correlation function, C(θ); and (2) missing power in the low multipole moments of the angular power spectrum, C_ℓ.

Aims. Their origin is still debated, however, due to a persistent lack of clarity concerning the seeding of quantum fluctuations in the early Universe. A likely explanation for the first of these appears to be a cutoff, k_min = (3.14 ± 0.36)×10⁻⁴ Mpc⁻¹, in the primordial power spectrum, 𝒫(k). Our goal in this paper is twofold: (1) we examine whether the same k_min can also self-consistently explain the missing power at large angles, and (2) we confirm that the introduction of this cutoff in 𝒫(k) does not adversely affect the remarkable consistency between the prediction of Planck-ΛCDM and the Planck measurements at ℓ > 30.

Methods. We have used the publicly available code CAMB to calculate the angular power spectrum, based on a line-of-sight approach. The code was modified slightly to include the additional parameter (i.e., k_min) characterizing the primordial power spectrum. In addition to this cutoff, the code optimized all of the usual standard-model parameters.

Results. In fitting the angular power spectrum, we found an optimized cutoff, k_min = (2.04_−0.79^+1.4) × 10⁻⁴ Mpc⁻¹, when using the whole range of ℓ’s, and k_min = (3.3_−1.3^+1.7) × 10⁻⁴ Mpc⁻¹, when fitting only the range ℓ ≤ 30, where the Sachs-Wolfe effect is dominant.

Conclusions. These are fully consistent with the value inferred from C(θ), suggesting that both of these large-angle anomalies may be due to the same truncation in 𝒫(k).