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We propose a novel bias-free method for reconstructing the power spectrum of the weak lensing deflection field from cosmic microwave background (CMB) observations. The proposed method is in contrast to the standard method of CMB lensing reconstruction where a reconstruction bias needs to be subtracted to estimate the lensing power spectrum. This bias depends very sensitively on the modeling of the signal and noise properties of the survey, and a misestimate can lead to significantly inaccurate results. Our method obviates this bias and hence the need to characterize the detailed noise properties of the CMB experiment. We illustrate our method with simulated lensed CMB maps with realistic noise distributions. This bias-free method can also be extended to create much more reliable estimators for other four-point functions in cosmology, such as those appearing in primordial non-Gaussianity estimators.
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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.
We present a method to measure the small-scale matter power spectrum using high-resolution measurements of the gravitational lensing of the Cosmic Microwave Background (CMB). To determine whether small-scale structure today is suppressed on scales below 10 kiloparsecs (corresponding to M < 10^9 M_sun), one needs to probe CMB-lensing modes out to L ~ 35,000, requiring a CMB experiment with about 20 arcsecond resolution or better. We show that a CMB survey covering 4,000 square degrees of sky, with an instrumental sensitivity of 0.5 uK-arcmin at 18 arcsecond resolution, could distinguish between cold dark matter and an alternative, such as 1 keV warm dark matter or 10^(-22) eV fuzzy dark matter with about 4-sigma significance. A survey of the same resolution with 0.1 uK-arcmin noise could distinguish between cold dark matter and these alternatives at better than 20-sigma significance; such high-significance measurements may also allow one to distinguish between a suppression of power due to either baryonic effects or the particle nature of dark matter, since each impacts the shape of the lensing power spectrum differently. CMB temperature maps yield higher signal-to-noise than polarization maps in this small-scale regime; thus, systematic effects, such as from extragalactic astrophysical foregrounds, need to be carefully considered. However, these systematic concerns can likely be mitigated with known techniques. Next-generation CMB lensing may thus provide a robust and powerful method of measuring the small-scale matter power spectrum.
We constrain the redshift dependence of gas pressure bias $leftlangle b_{y} P_{mathrm{e}}rightrangle$ (bias-weighted average electron pressure), which characterises the thermodynamics of intergalactic gas, through a combination of cross-correlations between galaxy positions and the thermal Sunyaev-Zeldovich (tSZ) effect, as well as galaxy positions and the gravitational lensing of the cosmic microwave background (CMB). The galaxy sample is from the fourth data release of the Kilo-Degree Survey (KiDS). The tSZ $y$ map and the CMB lensing map are from the {textit{Planck}} 2015 and 2018 data releases, respectively. The measurements are performed in five redshift bins with $zlesssim1$. With these measurements, combining galaxy-tSZ and galaxy-CMB lensing cross-correlations allows us to break the degeneracy between galaxy bias and gas pressure bias, and hence constrain them simultaneously. In all redshift bins, the best-fit values of $bpe$ are at a level of $sim 0.3, mathrm{meV/cm^3}$ and increase slightly with redshift. The galaxy bias is consistent with unity in all the redshift bins. Our results are not sensitive to the non-linear details of the cross-correlation, which are smoothed out by the {textit{Planck}} beam. Our measurements are in agreement with previous measurements as well as with theoretical predictions. We also show that our conclusions are not changed when CMB lensing is replaced by galaxy lensing, which shows the consistency of the two lensing signals despite their radically different redshift ranges. This study demonstrates the feasibility of using CMB lensing to calibrate the galaxy distribution such that the galaxy distribution can be used as a mass proxy without relying on the precise knowledge of the matter distribution.
The cosmological parameters prefered by the cosmic microwave background (CMB) primary anisotropies predict many more galaxy clusters than those that have been detected via the thermal Sunyaev-Zeldovich (tSZ) effect. This tension has attracted considerable attention since it could be evidence of physics beyond the simplest $Lambda$CDM model. However, an accurate and robust calibration of the mass-observable relation for clusters is necessary for the comparison, which has been proven difficult to obtain so far. Here, we present new contraints on the mass-pressure relation by combining tSZ and CMB lensing measurements about optically-selected clusters. Consequently, our galaxy cluster sample is independent from the data employed to derive cosmological constrains. We estimate an average hydrostatic mass bias of $b = 0.26 pm 0.07$, with no significant mass nor redshift evolution. This value greatly reduces the tension between the predictions of $Lambda$CDM and the observed abundance of tSZ clusters while being in agreement with recent estimations from tSZ clustering. On the other hand, our value for $b$ is higher than the predictions from hydro-dynamical simulations. This suggests the existence of mechanisms driving large departures from hydrostatic equilibrium and that are not included in state-of-the-art simulations, and/or unaccounted systematic errors such as biases in the cluster catalogue due to the optical selection.
The lensing power spectrum from cosmic microwave background (CMB) temperature maps will be measured with unprecedented precision with upcoming experiments, including upgrades to ACT and SPT. Achieving significant improvements in cosmological parameter constraints, such as percent level errors on sigma_8 and an uncertainty on the total neutrino mass of approximately 50 meV, requires percent level measurements of the CMB lensing power. This necessitates tight control of systematic biases. We study several types of biases to the temperature-based lensing reconstruction signal from foreground sources such as radio and infrared galaxies and the thermal Sunyaev-Zeldovich effect from galaxy clusters. These foregrounds bias the CMB lensing signal due to their non-Gaussian nature. Using simulations as well as some analytical models we find that these sources can substantially impact the measured signal if left untreated. However, these biases can be brought to the percent level if one masks galaxies with fluxes at 150 GHz above 1 mJy and galaxy clusters with masses above M_vir = 10^14 M_sun. To achieve such percent level bias, we find that only modes up to a maximum multipole of l_max ~ 2500 should be included in the lensing reconstruction. We also discuss ways to minimize additional bias induced by such aggressive foreground masking by, for example, exploring a two-step masking and in-painting algorithm.
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