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

Maresuke Shiraishi; Eiichiro Komatsu; Marco Peloso; Neil Barnaby

doi:10.1088/1475-7516/2013/05/002

paper

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

arXiv:1302.3056 · doi:10.1088/1475-7516/2013/05/002

Abstract

The bispectrum of primordial curvature perturbations in the squeezed configuration, in which one wavenumber, $k_{3}$ , is much smaller than the other two, $k_{3} ≪ k_{1} \approx k_{2}$ , 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 $k_{3}$ such that $B_{ζ} (k_{1}, k_{2}, k_{3}) \to 2 \sum_{L} c_{L} P_{L} (k^_{1} \cdot k^_{3}) P_{ζ} (k_{1}) P_{ζ} (k_{3})$ , where $P_{L}$ are the Legendre polynomials. While $c_{0}$ is related to the usual local-form $f_{NL}$ parameter as $c_{0} = 6 f_{NL} /5$ , the higher-multipole coefficients, $c_{1}$ , $c_{2}$ , etc., have not been constrained by the data. Primordial curvature perturbations sourced by large-scale magnetic fields generate non-vanishing $c_{0}$ , $c_{1}$ , and $c_{2}$ . Inflation models whose action contains a term like $I (ϕ)^{2} F^{2}$ generate $c_{2} = c_{0} /2$ . A recently proposed "solid inflation" model generates $c_{2} ≫ c_{0}$ . 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 $δ c_{0} = 4.4$ , $δ c_{1} = 61$ , and $δ c_{2} = 13$ (68% CL). We also find that $c_{0}$ and $c_{1}$ , and $c_{0}$ and $c_{2}$ , 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.

31 pages, 6 figures. Accepted for publication in JCAP

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

Abstract

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