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Abstract The cosmic microwave background (CMB) photons that scatter off free electrons in the large-scale structure induce a linear polarization pattern proportional to the remote CMB temperature quadrupole observed in the electrons' rest frame. The associated blackbody polarization anisotropies are known as the polarized Sunyaev Zel'dovich (pSZ) effect. Relativistic corrections to the remote quadrupole field give rise to a non-blackbody polarization anisotropy proportional to the square of the transverse peculiar velocity field; this is the kinetic polarized Sunyaev Zel'dovich (kpSZ) effect. In this paper, we forecast the ability of future CMB and galaxy surveys to detect the kpSZ effect, finding that a statistically significant detection is within the reach of planned experiments. We further introduce a quadratic estimator for the square of the peculiar velocity field based on a galaxy survey and CMB polarization. Finally, we outline how the kpSZ effect is a probe of cosmic birefringence and primordial non-Gaussianity, forecasting the reach of future experiments. 

Abstract We forecast the number of galaxy clusters that can be detected via the thermal Sunyaev–Zel’dovich (tSZ) signals by future cosmic microwave background (CMB) experiments, primarily the wide area survey of the CMB-S4 experiment but also CMB-S4's smaller de-lensing survey and the proposed CMB-HD experiment. We predict that CMB-S4 will detect 75,000 clusters with its wide survey of f sky = 50% and 14,000 clusters with its deep survey of f sky = 3%. Of these, approximately 1350 clusters will be at z ≥ 2, a regime that is difficult to probe by optical or X-ray surveys. We assume CMB-HD will survey the same sky as the S4-Wide, and find that CMB-HD will detect three times more overall and an order of magnitude more z ≥ 2 clusters than CMB-S4. These results include galactic and extragalactic foregrounds along with atmospheric and instrumental noise. Using CMB-cluster lensing to calibrate the cluster tSZ–mass scaling relation, we combine cluster counts with primary CMB to obtain cosmological constraints for a two-parameter extension of the standard model (ΛCDM + ∑ m ν + w 0 ). In addition to constraining σ ( w 0 ) to ≲1%, we find that both surveys can enable a ∼2.5–4.5 σ detection of ∑ m ν , substantially strengthening CMB-only constraints. We also study the evolution of the intracluster medium by modeling the cluster virialization v( z ) and find tight constraints from CMB-S4, with further factors of three to four improvement for CMB-HD. 

We present the tightest cosmic microwave background (CMB) lensing constraints to date on the growth of structure by combining CMB lensing measurements from the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT) and \textit{Planck}. Each of these surveys individually provides lensing measurements with similarly high statistical power, achieving signal-to-noise ratios of approximately 40. The combined lensing bandpowers represent the most precise CMB lensing power spectrum measurement to date with a signal-to-noise ratio of 61 and an amplitude of Areconlens=1.025±0.017 with respect to the theory prediction from the best-fit CMB \textit{Planck}-ACT cosmology. The bandpowers from all three lensing datasets, analyzed jointly, yield a 1.6% measurement of the parameter combination SCMBL8≡σ8(Ωm/0.3)0.25=0.825+0.015−0.013. Including Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data improves the constraint on the amplitude of matter fluctuations to σ8=0.829±0.009 (a 1.1% determination). When combining with uncalibrated supernovae from \texttt{Pantheon+}, we present a 4% sound-horizon-independent estimate of H0=66.4±2.5kms−1Mpc−1. The joint lensing constraints on structure growth and present-day Hubble rate are fully consistent with a ΛCDM model fit to the primary CMB data from \textit{Planck} and ACT. While the precise upper limit is sensitive to the choice of data and underlying model assumptions, when varying the neutrino mass sum within the ΛCDM cosmological model, the combination of primary CMB, BAO and CMB lensing drives the probable upper limit for the mass sum towards lower values, comparable to the minimum mass prior required by neutrino oscillation experiments.