Statistical anisotropies in temperature and polarization fluctuations from a scale-dependent trispectrum

TL;DR

This paper investigates how a scale-dependent local-type trispectrum can generate statistical anisotropies in CMB temperature and polarization, potentially explaining observed hemispherical power asymmetry and affecting spectral index measurements.

Contribution

It models the CMB power asymmetry using a local trispectrum with specific amplitude and tilt, and evaluates its observational signatures and constraints from Planck data.

Findings

Hemispherical power asymmetry can be explained by a local trispectrum with $ au_{NL} oughly 2 imes 10^4$ and tilt $n oughly -0.68$.

Non-Gaussian covariance impacts the measurement of the spectral index of primordial fluctuations.

The model predicts higher-order modulations and covariance effects that can distinguish it from other explanations.

Abstract

We study statistical anisotropies generated in the observed two-point function of the cosmic microwave background (CMB) fluctuations if the primordial statistics are non-Gaussian. Focusing on the dipole modulations of the anisotropies, we find that the hemispherical power asymmetry observed in the CMB temperature fluctuations can be modeled by a local-type trispectrum with amplitude $\tau_{\rm NL}(k_p=0.05~{\rm Mpc}^{-1}) \approx 2 \times 10^4$ and a large red tilt $n\approx -0.68$. We numerically evaluate the non-Gaussian covariance of the modulation estimators for both temperature and E-mode polarization fluctuations and discuss the prospects of constraining the model using Planck satellite data. We then discuss other effects of the scale-dependent trispectrum that could be used to distinguish this scenario from other explanations of the power asymmetry: higher-order modulations of the two-point function and the non-Gaussian angular power spectrum covariance. As an important consequence of the non-Gaussian power spectrum covariance, we discuss how the CMB-inferred spectral index of primordial scalar fluctuations can be significantly biased in the presence of a scale-dependent local-type trispectrum.