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

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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 k₁ and k₃ such that Bζ(k₁, k₂, k₃) → 2 ∑ₗ cₗ Pₗ(k₁ · k₃) Pζ(k₁)Pζ(k₃), where Pₗ 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)² F² 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 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.