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Testing deviations from the $Lambda$CDM model using the Cosmic Microwave Background (CMB) power spectra requires a pristine understanding of instrumental systematics. In this work we discuss the properties of a new observable ${cal R}^{TE}_{ell}$, the correlation coefficient of temperature and E modes. We find that this observable is mostly unaffected by systematics introducing multiplicative biases such as errors in calibration, polarisation efficiency, beam and transfer function measurements. We discuss the dependency of this observable on the cosmological model and derive its statistical properties. We then compute the T-E correlation coefficients of Planck legacy data and compare them with expectations from the Planck best-fit $Lambda$CDM and foreground model.
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Tensions in cosmological parameters measurement motivate a revisit of the effects of instrumental systematics. In this article, we focus on the Pearsons correlation coefficient of the cosmic microwave background temperature and polarization E modes $mathcal{R}_ell^{rm TE}$ which has the property of not being biased by multiplicative instrumental systematics. We build a $mathcal{R}_ell^{rm TE}$-based likelihood for the Planck data, and present the first constraints on $Lambda$CDM parameters from the correlation coefficient. Our results are compatible with parameters derived from a power spectra based likelihood. In particular the value of the Hubble parameter $H_0$ characterizing the expansion of the Universe today, 67.5 $pm$ 1.3 km/s/Mpc, is consistent with the ones inferred from standard CMB analysis. We also discuss the consistency of the Planck correlation coefficient with the one computed from the most recent ACTPol power spectra.
The European Space Agencys Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter LCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (theta_*) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the LCDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances.
We analyze the final release of the Planck satellite data to constrain the gravitational lensing potential in a model-independent manner. The amount of lensing determined from the smoothing of the acoustic peaks in the temperature and polarization power spectra is 2$sigma$ too high when compared with the measurements using the lensing reconstruction and 2.8$sigma$ too high when compared with $Lambda$CDM expectation based on the unlensed portion of the temperature and polarization power spectra. The largest change from the previous data release is the $Lambda$CDM expectation, driven by improved constraints to the optical depth to reionization. The anomaly still is inconsistent with actual gravitational lensing, given that the lensing reconstruction constraints are discrepant independent of the model. Within the context of $Lambda$CDM, improvements in its parameter constraints from lensing reconstruction bring this tension to 2.1$sigma$ and from further adding baryon acoustic oscillation and Pantheon supernova data to a marginally higher 2.2$sigma$. Once these other measurements are included, marginalizing this lensing-like anomaly cannot substantially resolve tensions with low-redshift measurements of $H_0$ and $S_8$ in $Lambda$CDM, $Lambda$CDM+$N_mathrm{eff}$ or $Lambda$CDM+$sum m_ u$; furthermore the artificial strengthening of constraints on $sum m_ u$ is less than 20%.
We present measurements of the $E$-mode ($EE$) polarization power spectrum and temperature-$E$-mode ($TE$) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg$^2$ region at 95, 150, and 220 GHz taken over a four month period in 2018. We report binned values of the $EE$ and $TE$ power spectra over the angular multipole range $300 le ell < 3000$, using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges $300 le ell le 1400$ for $EE$ and $300 le ell le 1700$ for $TE$, resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G dataset is well-fit by a $Lambda$CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find $H_0 = 68.8 pm 1.5 mathrm{km,s^{-1},Mpc^{-1}}$ and $sigma_8 = 0.789 pm 0.016$, with a gravitational lensing amplitude consistent with the $Lambda$CDM prediction ($A_L = 0.98 pm 0.12$). We combine the SPT-3G and the Planck datasets and obtain joint constraints on the $Lambda$CDM model. The volume of the 68% confidence region in six-dimensional $Lambda$CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with only slight shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.
The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70GHz and 100GHz channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70/100/143GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8deg-15arcmin are consistent with noise, and show no evidence of cosmic microwave background structure. Including small but important corrections for unresolved-source residuals, we demonstrate agreement between 70 and 100GHz power spectra averaged over 70<l<390 at the 0.8% level, and agreement between 143 and 100GHz power spectra of 0.4% over the same l range. These values are within and consistent with the overall uncertainties in calibration given in the Planck 2013 results. We also present results based on the 2013 likelihood analysis showing consistency at the 0.35% between the 100/143/217GHz power spectra. We analyse calibration procedures and beams to determine what fraction of these differences can be accounted for by known approximations or systematic errors that could be controlled even better in the future, reducing uncertainties still further. Several possible small improvements are described...(abridged)
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