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

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 B_ζ(k₁,k ₂,k₃) 2∑_LcLPL( _1·3)P_ζ(k₁)P _ζ(k₃), where P_L are the Legendre polynomials. While c₀ is related to the usual local-form f _NL parameter as c₀ = 6f_NL/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 = c_0/2. A recently proposed ''solid inflation'' model generates c₂ >> c₀. A cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to ℓ_max = 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.