A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope

TL;DR

This work measures the CMB damping tail with the South Pole Telescope at 150 GHz over $\sim$790 deg$^2$, covering $650<\ell<3000$, and combines these data with the seven-year WMAP results to constrain a spatially flat $\Lambda$CDM model. The analysis introduces a robust, beam- and transfer-function-aware pipeline to extract unbiased bandpowers and covariances, then uses MCMC to derive cosmological parameters, including $n_s=0.9663\pm0.0112$ (improved to $0.9668\pm0.0093$ with external data) and a strong lensing detection ($A^{0.65}_L=0.94\pm0.15$). Extensions probing damping-tail physics yield mild preferences for non-standard values: $r<0.21$, $\frac{dn_s}{d\ln k}=-0.024\pm0.013$, $Y_p=0.296\pm0.030$, and $N_{ m eff}=3.85\pm0.62$, though cluster data tend to pull these toward standard values. Overall, the results reinforce the LCDM paradigm while demonstrating the damping tail’s sensitivity to early-universe parameters and emphasizing the value of combining CMB with low-redshift measurements for tightening constraints.

Abstract

We present a measurement of the angular power spectrum of the cosmic microwave background (CMB) using data from the South Pole Telescope (SPT). The data consist of 790 square degrees of sky observed at 150 GHz during 2008 and 2009. Here we present the power spectrum over the multipole range 650 < ell < 3000, where it is dominated by primary CMB anisotropy. We combine this power spectrum with the power spectra from the seven-year Wilkinson Microwave Anisotropy Probe (WMAP) data release to constrain cosmological models. We find that the SPT and WMAP data are consistent with each other and, when combined, are well fit by a spatially flat, LCDM cosmological model. The SPT+WMAP constraint on the spectral index of scalar fluctuations is ns = 0.9663 +/- 0.0112. We detect, at ~5-sigma significance, the effect of gravitational lensing on the CMB power spectrum, and find its amplitude to be consistent with the LCDM cosmological model. We explore a number of extensions beyond the LCDM model. Each extension is tested independently, although there are degeneracies between some of the extension parameters. We constrain the tensor-to-scalar ratio to be r < 0.21 (95% CL) and constrain the running of the scalar spectral index to be dns/dlnk = -0.024 +/- 0.013. We strongly detect the effects of primordial helium and neutrinos on the CMB; a model without helium is rejected at 7.7-sigma, while a model without neutrinos is rejected at 7.5-sigma. The primordial helium abundance is measured to be Yp = 0.296 +/- 0.030, and the effective number of relativistic species is measured to be Neff = 3.85 +/- 0.62. The constraints on these models are strengthened when the CMB data are combined with measurements of the Hubble constant and the baryon acoustic oscillation feature. Notable improvements include ns = 0.9668 +/- 0.0093, r < 0.17 (95% CL), and Neff = 3.86 +/- 0.42. The SPT+WMAP data show...

Figures (13)

• Figure 1: The beam-deconvolved noise power in the SPT maps used in this analysis ( symbols show data and dotted line shows two-component model) compared to theoretical power spectra including CMB only ( dashed line) and CMB+foregrounds ( solid line). The precision of the power spectrum measurement is limited by sample variance rather than detector or atmospheric noise across most of the $650 < \ell < 3000$ range.
• Figure 2: A map of the ra3h30dec-60 field, which is typical of the fields used in this analysis. The effective area is 236 square degrees. The structure visible in this map is due to primary CMB anisotropy, not instrumental or atmospheric noise. Modes with $\ell \lesssim 600$ are strongly suppressed due to the high-pass filtering of the time-ordered data. The map has been multiplied by the apodization and point source masks described in Section \ref{['sec:windows']}, such that bright point sources with $S_{\rm{150 GHz}}>\ 50\ \rm{mJy}$ have been masked. A vertical stripe along the center of the map has been filtered more strongly than other regions. This stripe lies on the boundary of the lead and trail fields and is caused by high-pass filtering the time-ordered data by removing polynomial functions. This effect is accounted for in our analysis by using simulated observations.
• Figure 3: The $150$ GHz beam functions (bold, left scale) and fractional errors (thin, right scale). The beam function is normalized to one at $\ell=350$.
• Figure 4: The SPT power spectrum is shown in the left panel. The peak at $\ell\sim800$ is the third acoustic peak. For comparison we show in the right panel other recent measurements of the CMB damping tail from ACBAR reichardt09a, QUaD friedman09brown09, ACT das10, and SPT shirokoff11. The bandpower errors shown in these panels do not include beam or calibration uncertainties. The ACT spectrum extends to $\ell=10,000$. The previous SPT spectra, from lueker10 and shirokoff11, spanned the angular range $2000 < \ell < 10,000$ and targeted secondary CMB anisotropy.
• Figure 5: The SPT bandpowers, WMAP bandpowers, and best-fit $\Lambda$CDM theory spectrum shown with dashed (CMB) and solid (CMB+foregrounds) lines. The bandpower errors do not include beam or calibration uncertainties.