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Imprints of anisotropic inflation on the cosmic microwave background

Masa-aki Watanabe, Sugumi Kanno, Jiro Soda

TL;DR

This paper analyzes how anisotropic inflation imprints statistical anisotropy on the CMB temperature and polarization. It incorporates tensor perturbations and cross correlations with curvature perturbations, deriving off-diagonal two-point functions by decomposing primordial spectra with a preferred direction and explicit helicity bases. The authors present explicit expressions for the angular power spectra arising from scalar anisotropy, tensor anisotropy, cross correlation, and tensor linear polarization, outlining selection rules and parity considerations. They find that off-diagonal TB and EB signals, particularly from cross correlation, can be sizable and potentially observable, offering a distinctive signature of anisotropic inflation and motivating bipolar power spectrum analyses for detection.

Abstract

We study the imprints of anisotropic inflation on the CMB temperature fluctuations and polarizations. The statistical anisotropy stems not only from the direction dependence of curvature and tensor perturbations, but also from the cross correlation between curvature and tensor perturbations, and the linear polarization of tensor perturbations. We show that off-diagonal $TB$ and $EB$ spectrum as well as on- and off-diagonal $TT, EE, BB, TE$ spectrum are induced from anisotropic inflation. We emphasize that the off-diagonal spectrum induced by the cross correlation could be a characteristic signature of anisotropic inflation.

Imprints of anisotropic inflation on the cosmic microwave background

TL;DR

This paper analyzes how anisotropic inflation imprints statistical anisotropy on the CMB temperature and polarization. It incorporates tensor perturbations and cross correlations with curvature perturbations, deriving off-diagonal two-point functions by decomposing primordial spectra with a preferred direction and explicit helicity bases. The authors present explicit expressions for the angular power spectra arising from scalar anisotropy, tensor anisotropy, cross correlation, and tensor linear polarization, outlining selection rules and parity considerations. They find that off-diagonal TB and EB signals, particularly from cross correlation, can be sizable and potentially observable, offering a distinctive signature of anisotropic inflation and motivating bipolar power spectrum analyses for detection.

Abstract

We study the imprints of anisotropic inflation on the CMB temperature fluctuations and polarizations. The statistical anisotropy stems not only from the direction dependence of curvature and tensor perturbations, but also from the cross correlation between curvature and tensor perturbations, and the linear polarization of tensor perturbations. We show that off-diagonal and spectrum as well as on- and off-diagonal spectrum are induced from anisotropic inflation. We emphasize that the off-diagonal spectrum induced by the cross correlation could be a characteristic signature of anisotropic inflation.

Paper Structure

This paper contains 9 sections, 32 equations, 2 figures.

Table of Contents

  1. Introduction
  2. primordial statistical anisotropy
  3. Angular Power Spectra
  4. (i) anisotropy in scalar perturbations
  5. (ii) anisotropy in tensor perturbations
  6. (iii) cross correlation
  7. (iv)linear polarization
  8. discussion
  9. Definition of $\alpha_{lm}^{\pm 2,0},\beta_{lm}^{\pm 1}$

Figures (2)

  • Figure 1: The TT spectra induced by (i) anisotropy in scalar perturbations, (ii) that in tensor perturbations, (iii) cross correlation, and (iv) linear polarization of tensor perturbations. The parameters are chosen as $g=0.3,\ r=0.3$.
  • Figure 2: The TB and EB spectra induced by (iii) cross correlation. As a reference of magnitude, the conventional BB spectrum $l(l+1)C_{llmm}^{BB}/2\pi$ induced by isotropic part of the tensor perturbations is plotted with a dotted line. The parameters are chosen as $g=0.3,\ r=0.3$.