Cosmic microwave background (CMB) lensing from current and upcoming wide-field CMB experiments such as AdvACT, SPT-3G and Simons Observatory relies heavily on temperature (versus polarization). In this regime, foreground contamination to the temperature map produces significant lensing biases, which cannot be fully controlled by multifrequency component separation, masking, or bias hardening. In this Letter, we split the standard CMB lensing quadratic estimator into a new set of optimal "multipole" estimators. On large scales, these multipole estimators reduce to the known magnification and shear estimators, and a new shear B-mode estimator. We leverage the different symmetries of the lensed CMB and extragalactic foregrounds to argue that the shear-only estimator should be approximately immune to extragalactic foregrounds. We build a new method to compute, separately and without noise, the primary, secondary, and trispectrum biases to CMB lensing from foreground simulations. Using this method, we demonstrate that the shear estimator is, indeed, insensitive to extragalactic foregrounds, even when applied to a single-frequency temperature map contaminated with cosmic infrared background, thermal Sunyaev-Zel'dovich, kinematic Sunyaev-Zel'dovich, and radio point sources. This dramatic reduction in foreground biases allows us to include higher temperature multipoles than with the standard quadratic estimator, thus, increasing the total lensing signal-to-noise ratio beyond the quadratic estimator. In addition, magnification-only and shear B-mode estimators provide useful diagnostics for potential residuals.

CMB photons redshift and blueshift as they move through gravitational potentials $\Phi$ while propagating across the Universe. If the potential is not constant in time, the photons will pick up a net redshift or blueshift, known as the Integrated Sachs-Wolfe (ISW) effect. In the $z \ll 1000$ universe, $\dot{\Phi}$ is nonzero on large scales when the Universe transitions from matter to dark energy domination. This effect is only detectable in cross-correlation with large-scale structure at $z \sim 1$. In this paper we present a 3.2$\sigma$ detection of the ISW effect using cross-correlations between unWISE infrared galaxies and Planck CMB temperature maps. We use 3 tomographic galaxy samples spanning $0 < z < 2$, allowing us to fully probe the dark energy domination era and the transition into matter domination. This measurement is consistent with $\Lambda$CDM ($A_{\rm ISW} = 0.96 \pm 0.30$). We study constraints on a particular class of dynamical dark energy models (where the dark energy equation of state is different in matter and dark energy domination), finding that unWISE-ISW improves constraints from type Ia supernovae due to improved constraints on the time evolution of dark energy. When combining with BAO measurements, we obtain the tightest constraints on specific dynamical dark energy models. In the context of a phenomenological model for freezing quintessence, the Mocker model, we constrain the dark energy density within 10% at $z < 2$ using ISW, BAO and supernovae. Moreover, the ISW measurement itself provides an important independent check when relaxing assumptions about the theory of gravity, as it is sensitive to the gravitational potential rather than the expansion history.

Cross-correlations of CMB lensing reconstructions with other tracers of matter constrain primordial non-Gaussianity, neutrino masses and structure growth as a function of cosmic time. We formalize a method to improve the precision of these measurements by using a third tracer to remove structure from the lensing reconstructions. Crucially, our method enjoys the variance reduction benefits of a joint-modelling approach without the need to model the cosmological dependence of the ancillary tracer. We present a first demonstration of variance cancellation using data from Planck and the DESI Legacy Surveys, showing a 10-20% reduction in both lensing power and cross-correlation variance using the Cosmic Infrared Background (CIB) or DESI Legacy Survey Luminous Red Galaxies (LRGs) as matter tracers.

The search for primordial B-mode polarization of the cosmic microwave background (CMB) is limited by the sample variance of B-modes produced at later times by gravitational lensing. Constraints can be improved by "delensing": using some proxy of the matter distribution to partially remove the lensing-induced B-modes. Current and soon-upcoming experiments will infer a matter map - at least in part - from the temperature anisotropies of the CMB. These reconstructions are contaminated by extragalactic foregrounds: radio-emitting galaxies, the cosmic infrared background, or the Sunyaev-Zel'dovich effects. Using the Websky simulations, we show that the foregrounds add spurious power to the angular autospectrum of delensed B-modes via non-Gaussian higher-point functions, biasing constraints on the tensor-to-scalar ratio, r. We consider an idealized experiment similar to the Simons Observatory, with no Galactic or atmospheric foregrounds. After removing point sources detectable at 143 GHz and reconstructing lensing from CMB temperature modes l<3500 using a Hu-Okamoto quadratic estimator (QE), we infer a value of r that is 1.5σ higher than the true r=0. Reconstructing instead from a minimum-variance internal linear combination map only exacerbates the problem, bringing the bias above 3σ. When the TT estimator is co-added with other QEs or with external matter tracers, new couplings ensue which partially cancel the diluted bias from TT. We provide a simple and effective prescription to model these effects. In addition, we demonstrate that the point-source-hardened or shear-only QEs can not only mitigate the biases to acceptable levels but also lead to lower power than the Hu-Okamoto QE after delensing. Thus, temperature-based reconstructions remain powerful tools in the quest to measure r.

Gravitational lensing of the cosmic microwave background (CMB) is expected to be amongst the most powerful cosmological tools for ongoing and upcoming CMB experiments. In this work, we investigate a bias to CMB lensing reconstruction from temperature anisotropies due to the kinematic Sunyaev-Zel'dovich (kSZ) effect, that is, the Doppler shift of CMB photons induced by Compton scattering off moving electrons. The kSZ signal yields biases due to both its own intrinsic non-Gaussianity and its nonzero cross-correlation with the CMB lensing field (and other fields that trace the large-scale structure). This kSZ-induced bias affects both the CMB lensing autopower spectrum and its cross-correlation with low-redshift tracers. Furthermore, it cannot be removed by multifrequency foreground separation techniques because the kSZ effect preserves the blackbody spectrum of the CMB. While statistically negligible for current data sets, we show that it will be important for upcoming surveys, and failure to account for it can lead to large biases in constraints on neutrino masses or the properties of dark energy. For a stage 4 CMB experiment, the bias can be as large as ≈15% or 12% in cross-correlation with LSST galaxy lensing convergence or galaxy overdensity maps, respectively, when the maximum temperature multipole used in the reconstruction is lmax=4000, and about half of that when lmax=3000. Similarly, we find that the CMB lensing autopower spectrum can be biased by up to several percent. These biases are many times larger than the expected statistical errors. We validate our analytical predictions with cosmological simulations and present the first complete estimate of secondary-induced CMB lensing biases. The predicted bias is sensitive to the small-scale gas distribution, which is affected by pressure and feedback mechanisms, thus making removal via "bias-hardened" estimators challenging. Reducing lmax can significantly mitigate the bias at the cost of a decrease in the overall lensing reconstruction signal-to-noise. A bias ≲1% on large scales requires lmax≲2000, which leads to a reduction in signal-to-noise by a factor of ≈3-5 for a stage 4 CMB experiment. Polarization-only reconstruction may be the most robust mitigation strategy.

Patchy reionization leaves a number of imprints on the small-scale cosmic microwave background (CMB) temperature fluctuations, the largest of which is the kinematic Sunyaev-Zel'dovich (kSZ), the Doppler shift of CMB photons scattering off moving electrons in ionized bubbles. It has long been known that in the CMB power spectrum, this imprint of reionization is largely degenerate with the kSZ signal produced by late-time galaxies and clusters, thus limiting our ability to constrain reionization. Following Smith & Ferraro (2017), it is possible to isolate the reionization contribution in a model independent way, by looking at the large scale modulation of the small scale CMB power spectrum. In this paper we extend the formalism to use the full shape information of the small scale power spectrum (rather than just its broadband average), and argue that this is necessary to break the degeneracy between the optical depth τ and parameters setting the duration of reionization. In particular, we show that the next generation of CMB experiments could achieve up to a factor of 3 improvement on the optical depth τ and at the same time, constrain the duration of reionization to ∼25%. This can help tighten the constrains on neutrino masses, which will be limited by our knowledge of τ, and shed light on the physical processes responsible for reionization.

Upcoming cosmic microwave background (CMB) experiments will measure temperature fluctuations on small angular scales with unprecedented precision. Small-scale CMB fluctuations are a mixture of late-time effects: gravitational lensing, Doppler shifting of CMB photons by moving electrons [the kinematic Sunyaev-Zel'dovich (KSZ) effect], and residual foregrounds. We propose a new statistic which separates the KSZ signal from the others, and also allows the KSZ signal to be decomposed in redshift bins. The decomposition extends to high redshift and does not require external data sets such as galaxy surveys. In particular, the high-redshift signal from patchy reionization can be cleanly isolated, enabling future CMB experiments to make high-significance and qualitatively new measurements of the reionization era.

Extragalactic foregrounds are known to generate significant biases in temperature-based cosmic microwave background (CMB) lensing reconstruction. Several techniques, which include "source hardening"and "shear-only estimators"have been proposed to mitigate contamination and have been shown to be very effective at reducing foreground-induced biases. Here we extend both techniques to polarization, which will be an essential component of CMB lensing reconstruction for future experiments, and investigate the "large-lens"limit analytically to gain insight on the origin and scaling of foreground biases, as well as the sensitivity to their profiles. Using simulations of polarized point sources, we estimate the expected bias to both Simons Observatory and CMB-S4 like (polarization-based) lensing reconstruction, finding that biases to the former are minuscule while those to the latter are potentially non-negligible at small scales (L∼1000-2000). In particular, we show that for a CMB-S4 like experiment, an optimal linear combination of point-source hardened estimators can reduce the (point-source induced) bias to the CMB lensing power spectrum by up to two orders of magnitude, at a ∼4% noise cost relative to the global minimum variance estimator.

Abstract: Reconstructing the initial conditions of the Universe from late-time observations has the potential to optimally extract cosmological information. Due to the high dimensionality of the parameter space, a differentiable forward model is needed for convergence, and recent advances have made it possible to perform reconstruction with nonlinear models based on galaxy (or halo) positions. In addition to positions, future surveys will provide measurements of galaxies' peculiar velocities through the kinematic Sunyaev-Zel'dovich effect (kSZ), type Ia supernovae, the fundamental plane relation, and the Tully-Fisher relation. Here we develop the formalism for including halo velocities, in addition to halo positions, to enhance the reconstruction of the initial conditions. We show that using velocity information can significantly improve the reconstruction accuracy compared to using only the halo density field. We study this improvement as a function of shot noise, velocity measurement noise, and angle to the line of sight. We also show how halo velocity data can be used to improve the reconstruction of the final nonlinear matter overdensity and velocity fields. We have built our pipeline into the differentiable Particle-Mesh FlowPM package, paving the way to perform field-level cosmological inference with joint velocity and density reconstruction. This is especially useful given the increased ability to measure peculiar velocities in the near future.

A number of recent, low-redshift, lensing measurements hint at a universe in which the amplitude of lensing is lower than that predicted from the ?CDM model fit to the data of the Planck CMB mission. Here we use the auto- and cross-correlation signal of unWISE galaxies and Planck CMB lensing maps to infer cosmological parameters at low redshift. In particular, we consider three unWISE samples (denoted as "blue", "green"and "red") at median redshifts z ~ 0.6, 1.1 and 1.5, which fully cover the Dark Energy dominated era. Our cross-correlation measurements, with combined significance S/N ~ 80, are used to infer the amplitude of low-redshift fluctuations, s8; the fraction of matter in the Universe, O m ; and the combination S8 = s8 (O m /0.3)0.5 to which these low-redshift lensing measurements are most sensitive. The combination of blue, green and red samples gives a value S m = 0.784 ± 0.015, that is fully consistent with other low-redshift lensing measurements and in 2.4s tension with the CMB predictions from Planck. This is noteworthy, because CMB lensing probes the same physics as previous galaxy lensing measurements, but with very different systematics, thus providing an excellent complement to previous measurements.