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The Statistical Significance of the Low CMB Mulitipoles

G. Efstathiou

TL;DR

The paper tackles whether the WMAP observed low CMB quadrupole and octopole amplitudes require new physics beyond the concordance $\Lambda$CDM cosmology. It conducts both frequentist (power-spectrum based) and Bayesian analyses on WMAP plus external data, using a fiducial six-parameter flat $\Lambda$CDM model to gauge the significance of the low-\ell anomaly. The frequentist results show that the individual and joint low multipole amplitudes are not improbably small once sky cuts and foreground systematics are accounted for, while the Bayesian analysis finds only marginal evidence against the fiducial model, with odds sensitive to priors. The overall conclusion is that the low multipole data are compatible with $\Lambda$CDM, though exploring models with reduced large-scale power remains of interest and could be probed with improved estimators and foreground subtraction.

Abstract

The Wilkinson Microwave Anisotropy Probe (WMAP) has measured lower amplitudes for the temperature quadrupole and octopole anisotropies than expected in the best fitting (concordance) Lambda-dominated cold dark matter cosmology. Some authors have argued that this discrepancy may require new physics. Yet the statistical significance of this result is not clear. Some authors have applied frequentist arguments and claim that the discrepancy would occur by chance about 1 time in 700 if the concordance model is correct. Other authors have used Bayesian arguments to claim that the data show marginal evidence for new physics. I investigate these confusing and apparently conflicting claims using a frequentist analysis and a simplified Bayesian analysis. I conclude that the WMAP results are consistent with the concordance Lambda CDM model.

The Statistical Significance of the Low CMB Mulitipoles

TL;DR

The paper tackles whether the WMAP observed low CMB quadrupole and octopole amplitudes require new physics beyond the concordance CDM cosmology. It conducts both frequentist (power-spectrum based) and Bayesian analyses on WMAP plus external data, using a fiducial six-parameter flat CDM model to gauge the significance of the low-\ell anomaly. The frequentist results show that the individual and joint low multipole amplitudes are not improbably small once sky cuts and foreground systematics are accounted for, while the Bayesian analysis finds only marginal evidence against the fiducial model, with odds sensitive to priors. The overall conclusion is that the low multipole data are compatible with CDM, though exploring models with reduced large-scale power remains of interest and could be probed with improved estimators and foreground subtraction.

Abstract

The Wilkinson Microwave Anisotropy Probe (WMAP) has measured lower amplitudes for the temperature quadrupole and octopole anisotropies than expected in the best fitting (concordance) Lambda-dominated cold dark matter cosmology. Some authors have argued that this discrepancy may require new physics. Yet the statistical significance of this result is not clear. Some authors have applied frequentist arguments and claim that the discrepancy would occur by chance about 1 time in 700 if the concordance model is correct. Other authors have used Bayesian arguments to claim that the data show marginal evidence for new physics. I investigate these confusing and apparently conflicting claims using a frequentist analysis and a simplified Bayesian analysis. I conclude that the WMAP results are consistent with the concordance Lambda CDM model.

Paper Structure

This paper contains 5 sections, 6 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Observations and Fiducial Concordance Model
  3. Frequentist Statistics
  4. Bayesian Statistics
  5. Conclusions

Figures (3)

  • Figure 1: The histogram shows the quadrupole amplitudes for a sample of MCMC chains for a six parameter $\Lambda$CDM fit to WMAP+CBI+ACBAR+VSA data. The vertical dashed line shows the quadrupole amplitude observed by WMAP.
  • Figure 2: Histogram of quadrupole amplitudes estimated using a pseudo-$C_\ell$ estimator applied to $10^5$ simulations with a Galactic cut of $\pm 10^\circ$ centred on the Galactic plane. The power spectrum of the fiducial $\Lambda$CDM model discussed in Section 2 was used to generate the simulations. The solid line shows a $\chi^2$ distribution (equation 2) and the dashed line shows the quadrupole amplitude measured by WMAP.
  • Figure 3: Unnormalised Bayesian probability distributions for the quadrupole and octopole amplitudes given by equation (\ref{['B2']}). The dashed lines show the values for the fiducial $\Lambda$CDM model discussed in Section 2.