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CMB Anomalies from Relic Anisotropy

A. E. Gumrukcuoglu, Carlo R. Contaldi, Marco Peloso

TL;DR

This work investigates potential CMB anomalies arising from relic anisotropy by proposing a direction-dependent primordial power spectrum with axisymmetry. The authors derive a generalized CMB covariance matrix that encodes correlations between different multipoles induced by the directional spectrum and analyze how axisymmetry constrains these correlations. They present a concrete background model with an initial anisotropic expansion that isotropizes during inflation, showing that large-scale modes can retain imprints of the early anisotropy. By focusing on longitudinal perturbations, they derive a Mukhanov-Sasaki-like equation whose solutions reveal standard behavior for horizon-exited modes during isotropic inflation and nonstandard spectra for modes that left during the anisotropic phase, providing a falsifiable link between early-universe anisotropy and observable CMB anomalies.

Abstract

Most of the analysis of the Cosmic Microwave Background relies on the assumption of statistical isotropy. However, given some recent evidence pointing against isotropy, as for instance the observed alignment of different multipoles on large scales, it is worth testing this assumption against the increasing amount of available data. As a pivot model, we assume that the spectrum of the primordial perturbations depends also on their directionality (rather than just on the magnitude of their momentum, as in the standard case). We explicitly compute the correlation matrix for the temperature anisotropies in the simpler case in which there is a residual isotropy between two spatial directions. As a concrete example, we consider a different initial expansion rate along one direction, and the following isotropization which takes place during inflation. Depending on the amount of inflation, this can lead to broken statistical isotropy on the largest observable scales.

CMB Anomalies from Relic Anisotropy

TL;DR

This work investigates potential CMB anomalies arising from relic anisotropy by proposing a direction-dependent primordial power spectrum with axisymmetry. The authors derive a generalized CMB covariance matrix that encodes correlations between different multipoles induced by the directional spectrum and analyze how axisymmetry constrains these correlations. They present a concrete background model with an initial anisotropic expansion that isotropizes during inflation, showing that large-scale modes can retain imprints of the early anisotropy. By focusing on longitudinal perturbations, they derive a Mukhanov-Sasaki-like equation whose solutions reveal standard behavior for horizon-exited modes during isotropic inflation and nonstandard spectra for modes that left during the anisotropic phase, providing a falsifiable link between early-universe anisotropy and observable CMB anomalies.

Abstract

Most of the analysis of the Cosmic Microwave Background relies on the assumption of statistical isotropy. However, given some recent evidence pointing against isotropy, as for instance the observed alignment of different multipoles on large scales, it is worth testing this assumption against the increasing amount of available data. As a pivot model, we assume that the spectrum of the primordial perturbations depends also on their directionality (rather than just on the magnitude of their momentum, as in the standard case). We explicitly compute the correlation matrix for the temperature anisotropies in the simpler case in which there is a residual isotropy between two spatial directions. As a concrete example, we consider a different initial expansion rate along one direction, and the following isotropization which takes place during inflation. Depending on the amount of inflation, this can lead to broken statistical isotropy on the largest observable scales.

Paper Structure

This paper contains 4 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction and discussion
  2. CMB covariance matrix
  3. Background evolution
  4. Perturbations

Figures (2)

  • Figure 1: Evolution of the Hubble rates and the difference in e-foldings during the anisotropic and the following isotropic inflationary stages. We have chosen a chaotic inflationary model, with quadratic potential $V = m_\phi^2 \phi^2 / 2$ with initial conditions $\phi_0 = 16 \,, h_0 = 10^4 \, m_\phi \,$. This leads to about $60$ e-foldings during the isotropic inflationary stage.
  • Figure 2: Power spectrum for longitudinal scalar perturbations. The initial conditions for the background are as in figure \ref{['fig:fig1']}, while $\phi =3$ at the moment shown here.