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Is the Low CMB Quadrupole a Signature of Spatial Curvature?

G. Efstathiou

TL;DR

This paper examines whether the anomalously low CMB quadrupole can be explained by spatial curvature within a closed universe. It shows that, while WMAP data strongly favor a flat ΛCDM model at high multipoles, closed models can remain consistent with the observations when the primordial power spectrum is truncated near the curvature scale. A curvature-scale truncation naturally suppresses the quadrupole and octopole in modestly closed models, linking the low-l anomalies to the curvature scale rather than requiring exotic topology. The authors emphasize the geometrical degeneracy in CMB data and argue that pinning down curvature will require additional astrophysical data, noting that a positively curved universe would have profound implications for inflationary theory.

Abstract

The temperature anisotropy power spectrum measured with the Wilkinson Microwave Anisotropy Probe (WMAP) at high multipoles is in spectacular agreement with an inflationary Lambda-dominated cold dark matter cosmology. However, the low order multipoles (especially the quadrupole) have lower amplitudes than expected from this cosmology, indicating a need for new physics. Here we speculate that the low quadrupole amplitude is associated with spatial curvature. We show that positively curved models are consistent with the WMAP data and that the quadrupole amplitude can be reproduced if the primordial spectrum truncates on scales comparable to the curvature scale.

Is the Low CMB Quadrupole a Signature of Spatial Curvature?

TL;DR

This paper examines whether the anomalously low CMB quadrupole can be explained by spatial curvature within a closed universe. It shows that, while WMAP data strongly favor a flat ΛCDM model at high multipoles, closed models can remain consistent with the observations when the primordial power spectrum is truncated near the curvature scale. A curvature-scale truncation naturally suppresses the quadrupole and octopole in modestly closed models, linking the low-l anomalies to the curvature scale rather than requiring exotic topology. The authors emphasize the geometrical degeneracy in CMB data and argue that pinning down curvature will require additional astrophysical data, noting that a positively curved universe would have profound implications for inflationary theory.

Abstract

The temperature anisotropy power spectrum measured with the Wilkinson Microwave Anisotropy Probe (WMAP) at high multipoles is in spectacular agreement with an inflationary Lambda-dominated cold dark matter cosmology. However, the low order multipoles (especially the quadrupole) have lower amplitudes than expected from this cosmology, indicating a need for new physics. Here we speculate that the low quadrupole amplitude is associated with spatial curvature. We show that positively curved models are consistent with the WMAP data and that the quadrupole amplitude can be reproduced if the primordial spectrum truncates on scales comparable to the curvature scale.

Paper Structure

This paper contains 4 sections, 7 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Constraints on Spatial Curvature and the Geometrical Degeneracy
  3. Low CMB multipoles and Spatial Curvature
  4. Conclusions

Figures (2)

  • Figure 1: Illustration of the geometrical degeneracy.The filled circles show the WMAP temperature power spectrum estimates. The nearly degenerate models with $\Omega_k=0.0$, $-0.05$, $-0.10$ and $-0.20$ (see Table 1) are shown by the solid lines and are identical except for minor differences at low multipoles. The error bars on the WMAP points use the theoretical power spectrum for the $\Omega_k=0$ model.
  • Figure 2: Low order CMB multipoles measured by WMAP: upper panel shows the temperature power spectrum and lower panel shows the temperature-polarization cross power-spectrum. The solid line shows the reference $\Omega_k=0.0$ model which has been used to calculate the error bars. The dashed, dotted and dot-dashed lines show the results for the positively curved models with the heuristic spectrum of equation (4b).