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

Abstract

The bispectrum of primordial curvature perturbations in the squeezed configuration, in which one wavenumber, $k_3$, is much smaller than the other two, $k_3\ll k_1\approx k_2$, 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 ${\mathbf{k}}_1$ and ${\mathbf{k}}_3$ such that $B_{\zeta }(k_1,k_2,k_3)\to 2{\sum }_L{c}_L{P}_L({\hat{\mathbf{k}}}_1\cdot {\hat{\mathbf{k}}}_3)P_{\zeta }(k_1)P_{\zeta }(k_3)$, where $P_L$ are the Legendre polynomials. While $c_0$ is related to the usual local-form $f_{\mathrm{NL}}$ parameter as $c_0=6f_{\mathrm{NL}}/5$, 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 $I(\varphi {)}^2{F}^2$ generate $c_2=c_0/2$. A recently proposed "solid inflation" model generates $c_2\gg c_0$. A cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to ${\ell }_{\max }=2000$ is able to measure these coefficients down to $\delta c_0=4.4$, $\delta c_1=61$, and $\delta c_2=13$ (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.

Comments: 31 pages, 6 figures. Accepted for publication in JCAP