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

TL;DR

This paper investigates how anisotropic sources during inflation influence the squeezed-limit bispectrum of the cosmic microwave background, introducing new angular-dependent coefficients that can reveal physics beyond standard models.

Contribution

It introduces a phenomenological angular dependence in the squeezed-limit bispectrum, constrains higher-multipole coefficients, and explores their implications for inflationary physics.

Findings

Higher-multipole coefficients can be constrained by CMB data.

Certain inflation models predict specific relations among these coefficients.

Measurement of these coefficients can reveal the presence of vector fields or complex symmetries during inflation.

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 ${\bf k}_1$ and ${\bf k}_3$ such that $B_\zeta(k_1, k_2, k_3) \to 2 \sum_L c_L P_L(\hat{\bf k}_1 \cdot \hat{\bf k}_3) P_\zeta(k_1)P_\zeta(k_3)$, where $P_L$ are the Legendre polynomials. While $c_0$ is related to the usual local-form $f_{\rm NL}$ parameter as $c_0=6f_{\rm NL}/5$, 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 $I(\phi)^2 F^2$ 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 $\ell_{\rm max}=2000$ 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.