Foregrounds and Forecasts for the Cosmic Microwave Background

TL;DR

This paper develops a comprehensive, physics-based framework to forecast how microwave foregrounds affect CMB parameter estimation for Boomerang, MAP, and Planck. It introduces a multi-component foreground model with frequency dependence $\Theta_{(k)}^P(\nu)$, frequency coherence $\xi_{(k)}^P$, and angular power spectra $C_{\ell(k)}^P$, and treats these components as a correlated noise source to be jointly estimated with cosmological parameters. Using a minimum-variance foreground removal and Fisher-matrix formalism, it finds that most cosmological parameters experience less than a factor of 2 degradation under a main foreground model, with larger (but still manageable) effects for large-angle polarization and more pessimistic scenarios. The analysis highlights vibrating dust and point-source contamination as the most damaging foregrounds and shows that cross-correlations between polarized and unpolarized foregrounds carry substantial polarization information. The results guide mission planning and foreground studies, demonstrating Planck’s robustness under realistic assumptions and underscoring the value of measuring foreground statistics from data and incorporating cross-channel information.

Abstract

One of the main challenges facing upcoming CMB experiments will be to distinguish the cosmological signal from foreground contamination. We present a comprehensive treatment of this problem and study how foregrounds degrade the accuracy with which the Boomerang, MAP and Planck experiments can measure cosmological parameters. Our foreground model includes not only the normalization, frequency dependence and scale dependence for each physical component, but also variations in frequency dependence across the sky. When estimating how accurately cosmological parameter can be measured, we include the important complication that foreground model parameters (we use about 500) must be simultaneously measured from the data as well. Our results are quite encouraging: despite all these complications, precision measurements of most cosmological parameters are degraded by less than a factor of 2 for our main foreground model and by less than a factor of 5 in our most pessimistic scenario. Parameters measured though large-angle polarization signals suffer more degradation: up to 5 in the main model and 25 in the pessimistic case. The foregrounds that are potentially most damaging and therefore most in need of further study are vibrating dust emission and point sources, especially those in the radio frequencies. It is well-known that E and B polarization contain valuable information about reionization and gravity waves, respectively. However, the cross-correlation between polarized and unpolarized foregrounds also deserves further study, as we find that it carries the bulk of the polarization information about most other cosmological parameters.

Figures (26)

• Figure 1: The MID model for synchrotron radiation (heavy line). The first three columns show the uncleaned amplitude as a function of scale at 30, 100 and 217 GHz. The rows show the temperature ($T$), cross-correlation ($X$) and $E$-channel polarization, respectively. For reference, the CMB power spectrum of our our fiducial $\Lambda$CDM cosmology (§ \ref{['CosmologyDef']}) is also shown (thin solid line) together with the total foreground power including (dotted) and excluding (dashed) Planck detector noise. The second three columns show the foregrounds amplitude when the maps are cleaned according to the optimal procedure in § \ref{['ResidualSec']}; this method assumes that the foreground properties are well-known. The cleaning depends on the experimental specifications; we show results for Boomerang, MAP and Planck. There is no polarization data in the Boomerang column, since this in an unpolarized experiment.
• Figure 2: Same as Fig. \ref{['SynchFig']}, but for free-free emission.
• Figure 3: Same as Fig. \ref{['SynchFig']}, but for thermal (vibrational) dust emission.
• Figure 4: Same as Fig. \ref{['SynchFig']}, but for thermal spinning dust emission.
• Figure 5: Same as Fig. \ref{['SynchFig']}, but for the thermal SZ effect from filaments.