Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background

Maresuke Shiraishi, Eiichiro Komatsu, Marco Peloso, Neil Barnaby

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The bispectrum of primordial curvature perturbations in the squeezed configuration, in which one wavenumber, k3, is much smaller than the other two, k3 << k1 k2, plays a special role in constraining the physics of inflation. In this paper we study a new phenomenological signature in the squeezed-limit bispectrum: namely, the amplitude of the squeezed-limit bispectrum depends on an angle between k 1 and k3 such that Bζ(k1,k 2,k3) 2∑LcLPL( 1·3)Pζ(k1)P ζ(k3), where PL are the Legendre polynomials. While c0 is related to the usual local-form f NL parameter as c0 = 6fNL/5, the higher-multipole coefficients, c1, c2, etc., have not been constrained by the data. Primordial curvature perturbations sourced by large-scale magnetic fields generate non-vanishing c0, c1, and c2. Inflation models whose action contains a term like I(φ)2F2 generate c2 = c0/2. A recently proposed ''solid inflation'' model generates c2 >> c0. A cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to ℓmax = 2000 is able to measure these coefficients down to δc0 = 4.4, δc1 = 61, and δc2 = 13 (68% CL). We also find that c0 and c1, and c0 and c2, are nearly uncorrelated. Measurements of these coefficients will open up a new window into the physics of inflation such as the existence of vector fields during inflation or non-trivial symmetry structure of inflaton fields. Finally, we show that the original form of the Suyama-Yamaguchi inequality does not apply to the case involving higher-spin fields, but a generalized form does.

Original languageEnglish (US)
Article number002
JournalJournal of Cosmology and Astroparticle Physics
Issue number5
StatePublished - May 2013


  • cosmological perturbation theory
  • inflation
  • non-gaussianity
  • primordial magnetic fields

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