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

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 ${\tau }_{\mathrm{NL}}(k_p=0.05{\mathrm{Mpc}}^{-1})\approx 2\times 10^4$ 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.

arXiv comment11 pages, 4 figures; v2: minor edits to match PRD version

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• Challenges for $\Lambda$CDM: An update
• Clustering of Local Extrema in Planck CMB maps
• Constraints on ${\tau }_{\mathrm{NL}}$ from Planck temperature and polarization
• Revisiting the large-scale CMB anomalies: The impact of the SZ signal from the Local Universe
• Isotropic non-Gaussian $g_{\mathrm{NL}}$-like toy models that reproduce the cosmic microwave background anomalies
• CMB Polarization by the Asymmetric Template of Scalar Perturbations
• Viable Curvaton Models from the $f_{NL}$ Parameter