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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%.
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We investigate correlations induced by gravitational lensing on simulated cosmic microwave background data of experiments with an incomplete sky coverage and their effect on inferences from the South Pole Telescope data. These correlations agree well with the theoretical expectations, given by the sum of super-sample and intra-sample lensing terms, with only a typically negligible $sim$ 5% discrepancy in the amplitude of the super-sample lensing effect. Including these effects we find that lensing constraints are in $3.0sigma$ or $2.1sigma$ tension between the SPT polarization measurements and Planck temperature or lensing reconstruction constraints respectively. If the lensing-induced covariance effects are neglected, the significance of these tensions increases to $3.5sigma$ or $2.5sigma$. Using the standard scaling parameter $A_L$ substantially underestimates the significance of the tension once other parameters are marginalized over. By parameterizing the super-sample lensing through the mean convergence in the SPT footprint, we find a hint of underdensity in the SPT region. We also constrain extra sharpening of the CMB acoustic peaks due to missing smoothing of the peaks by super-sample lenses at a level that is much smaller than the lens sample variance. Finally, we extend the usual shift in the means statistic for evaluating tensions to non-Gaussian posteriors, generalize an approach to extract correlation modes from noisy simulated covariance matrices, and present a treatment of correlation modes not as data covariances but as auxiliary model parameters.
Cross-correlations between the lensing of the cosmic microwave background (CMB) and other tracers of large-scale structure provide a unique way to reconstruct the growth of dark matter, break degeneracies between cosmology and galaxy physics, and test theories of modified gravity. We detect a cross-correlation between DESI-like luminous red galaxies (LRGs) selected from DECaLS imaging and CMB lensing maps reconstructed with the Planck satellite at a significance of $S/N = 27.2$ over scales $ell_{rm min} = 30$, $ell_{rm max} = 1000$. To correct for magnification bias, we determine the slope of the LRG cumulative magnitude function at the faint limit as $s = 0.999 pm 0.015$, and find corresponding corrections on the order of a few percent for $C^{kappa g}_{ell}, C^{gg}_{ell}$ across the scales of interest. We fit the large-scale galaxy bias at the effective redshift of the cross-correlation $z_{rm eff} approx 0.68$ using two different bias evolution agnostic models: a HaloFit times linear bias model where the bias evolution is folded into the clustering-based estimation of the redshift kernel, and a Lagrangian perturbation theory model of the clustering evaluated at $z_{rm eff}$. We also determine the error on the bias from uncertainty in the redshift distribution; within this error, the two methods show excellent agreement with each other and with DESI survey expectations.
The overall cosmological parameter tension between the Atacama Cosmology Telescope 2020 (ACT) and Planck 2018 data within the concordance cosmological model is quantified using the suspiciousness statistic to be 2.6$sigma$. Between ACT and the South Pole Telescope (SPT) we find a tension of 2.4$sigma$, and 2.8$sigma$ between ACT and Planck+SPT combined. While it is unclear whether the tension is caused by statistical fluctuations, systematic effects or new physics, caution should be exercised in combining these cosmic microwave background datasets in the context of the $Lambda$CDM standard model of the universe.
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.
The angular power spectra of the cosmic microwave background (CMB) temperature anisotropies reconstructed from Planck data seem to present too much gravitational lensing distortion. This is quantified by the control parameter $A_L$ that should be compatible with unity for a standard cosmology. With the Class Boltzmann solver and the profile-likelihood method, for this parameter we measure a 2.6$sigma$ shift from 1 using the Planck public likelihoods. We show that, owing to strong correlations with the reionization optical depth $tau$ and the primordial perturbation amplitude $A_s$, a $sim2sigma$ tension on $tau$ also appears between the results obtained with the low ($ellleq 30$) and high ($30<elllesssim 2500$) multipoles likelihoods. With Hillipop, another high-$ell$ likelihood built from Planck data, this difference is lowered to $1.3sigma$. In this case, the $A_L$ value is still in disagreement with unity by $2.2sigma$, suggesting a non-trivial effect of the correlations between cosmological and nuisance parameters. To better constrain the nuisance foregrounds parameters, we include the very high $ell$ measurements of the Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT) experiments and obtain $A_L = 1.03 pm 0.08$. The Hillipop+ACT+SPT likelihood estimate of the optical depth is $tau=0.052pm{0.035,}$ which is now fully compatible with the low $ell$ likelihood determination. After showing the robustness of our results with various combinations, we investigate the reasons for this improvement that results from a better determination of the whole set of foregrounds parameters. We finally provide estimates of the $Lambda$CDM parameters with our combined CMB data likelihood.
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