Hint of a truncated primordial spectrum from the CMB large-scale anomalies
Fulvio Melia, Qing-Bo Ma, Jun-Jie Wei, Bo Yu
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 ).