Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background (1302.3056v2)

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.

Signatures of Anisotropic Sources in the Squeezed-Limit Bispectrum of the Cosmic Microwave Background

This paper addresses the bispectrum analysis of primordial curvature perturbations, specifically focusing on the squeezed-limit configuration where one wavenumber is much smaller than the other two. The authors investigate how this bispectrum depends on the angular positioning of these wavenumbers, particularly under the influence of anisotropic sources. This approach provides new insights into the physics of the early universe, notably during the inflationary epoch.

The paper proposes a parametrization of the bispectrum in the squeezed limit through a functional form characterized by Legendre polynomials. The coefficients derived from these polynomials serve as markers for potential anisotropic sources during inflation, such as large-scale magnetic fields or vector fields. Notably, these coefficients provide an angular dependence, unprecedented in existing data analyses, rendering it a novel probe into inflaton field symmetries or the existence of vector fields during inflation.

The analysis reveals that, while the monopole term corresponds to the conventional local-form non-Gaussian parameter $f_{NL}$, higher multipole components arise from more exotic initial conditions. Models such as solid inflation, characterized by elasticity-induced anisotropies, and vector-field couplings to curvature perturbations, exemplify scenarios yielding non-trivial angular dependence in the bispectrum.

Numerically, cosmic microwave background (CMB) data from a cosmic-variance-limited experiment could determine these coefficients with notable precision: $\delta c_0 \approx 4.4$, $\delta c_1 \approx 61$, and $\delta c_2 \approx 13$. This capability to isolate terms related to higher-spin fields substantially enriches the toolkit for inflationary model verification. Moreover, the paper postulates that while $c_0$ relates directly to the local non-Gaussian parameter $f_{NL}$, coefficients like $c_2$ pertain to the quadrupole moment and highlight the potential influence of anisotropic stress in the early universe.

The implications of this approach extend beyond theoretical frameworks to the practical field of observational astronomy. Observing these angular dependencies in CMB bispectra could unveil unprecedented information about the early universe's vector fields or residual inflaton interactions. Furthermore, such investigations highlight the robustness of symmetry conditions and their impact on existing inflationary models.

The posture concerning the Suyama-Yamaguchi inequality is particularly intriguing; it suggests modifications in scenarios involving higher-spin fields. This broader inequality becomes pertinent in ascertaining the necessary conditions for trispectrum-bispectrum consistency, contributing another layer to our understanding of primordial non-Gaussianity.

In conclusion, this paper sets forth a significant methodological advance in examining anisotropic signatures in the CMB bispectrum. It opens new avenues for investigating angular dependencies in primordial curvature perturbations and enhances our understanding of early universe dynamics. Future work could focus on real CMB datasets from missions like the Planck satellite to see if these analytical forecasts hold true, thereby testing the observational validity of these theoretical predictions. This line of research holds promise for shedding light on the intricate physics governing the universe's formative epochs.