We present tomographic measurements of structure growth using crosscorrelations of Atacama Cosmology Telescope (ACT) DR6 and Planck cosmic microwave background (CMB) lensing maps with the unWISE Blue and Green galaxy samples, which span the redshift ranges 0.2 ≲
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Abstract z ≲ 1.1 and 0.3 ≲z ≲ 1.8, respectively. We improve on prior unWISE crosscorrelations not just by making use of the new, highprecision ACT DR6 lensing maps, but also by including additional spectroscopic data for redshift calibration and by analyzing our measurements with a more flexible theoretical model. We determine the amplitude of matter fluctuations at low redshifts (z ≃ 0.2–1.6), finding using the ACT crosscorrelation alone and ${S}_{8}\equiv {\sigma}_{8}{({\mathrm{\Omega}}_{m}/0.3)}^{0.5}=0.813\pm 0.021$S _{8}= 0.810 ± 0.015 with a combination of Planck and ACT crosscorrelations; these measurements are fully consistent with the predictions from primary CMB measurements assuming standard structure growth. The addition of baryon acoustic oscillation data breaks the degeneracy betweenσ _{8}and Ω_{m}, allowing us to measureσ _{8}= 0.813 ± 0.020 from the crosscorrelation of unWISE with ACT andσ _{8}= 0.813 ± 0.015 from the combination of crosscorrelations with ACT and Planck. These results also agree with the expectations from primary CMB extrapolations in ΛCDM cosmology; the consistency ofσ _{8}derived from our two redshift samples atz ∼ 0.6 and 1.1 provides a further check of our cosmological model. Our results suggest that structure formation on linear scales is well described by ΛCDM even down to low redshiftsz ≲ 1. 
ABSTRACT We seek to clarify the origin of constraints on the dark energy equation of state parameter from CMB lensing tomography, that is the combination of galaxy clustering and the crosscorrelation of galaxies with CMB lensing in a number of redshift bins. We focus on the analytic understanding of the origin of the constraints. Dark energy information in these data arises from the influence of three primary relationships: distance as a function of redshift (geometry), the amplitude of the power spectrum as a function of redshift (growth), and the power spectrum as a function of wavenumber (shape). We find that the effects from geometry and growth play a significant role and partially cancel each other out, while the shape effect is unimportant. We also show that Dark Energy Task Force figure of merit forecasts from the combination of LSST galaxies and CMBS4 lensing are comparable to the forecasts from cosmic shear in the absence of the CMB lensing map, thus providing an important independent check. Compared to the forecasts with the LSST galaxies alone, combining CMB lensing and LSST clustering information increases the FoM by roughly a factor of 3–4 in the optimistic scenario where systematics are fully under control. We caution that achieving these forecasts will likely require a full analysis of higherorder biasing, photometric redshift uncertainties, and stringent control of other systematic limitations, which are outside the scope of this work, whose primary purpose is to elucidate the physical origin of the constraints.

Abstract We present cosmological constraints from a gravitational lensing mass map covering 9400 deg^{2}reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitude
σ _{8}= 0.819 ± 0.015 at 1.8% precision, , and the Hubble constant ${S}_{8}\equiv {\sigma}_{8}{({\mathrm{\Omega}}_{\mathrm{m}}/0.3)}^{0.5}=0.840\pm 0.028$H _{0}= (68.3 ± 1.1) km s^{−1}Mpc^{−1}at 1.6% precision. A joint constraint with Planck CMB lensing yieldsσ _{8}= 0.812 ± 0.013, , and ${S}_{8}\equiv {\sigma}_{8}{({\mathrm{\Omega}}_{\mathrm{m}}/0.3)}^{0.5}=0.831\pm 0.023$H _{0}= (68.1 ± 1.0) km s^{−1}Mpc^{−1}. These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find thatS _{8}from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σ to 2.1σ . This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probingz ∼ 0.5–5 on mostly linear scales and galaxy lensing atz ∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑m _{ν}< 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of crosscorrelation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming groundbased CMB surveys. 
Abstract We present new measurements of cosmic microwave background (CMB) lensing over 9400 deg^{2}of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB data set, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at 2.3% precision (43
σ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure that our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. Our CMB lensing power spectrum measurement provides constraints on the amplitude of cosmic structure that do not depend on Planck or galaxy survey data, thus giving independent information about largescale structure growth and potential tensions in structure measurements. The baseline spectrum is well fit by a lensing amplitude ofA _{lens}= 1.013 ± 0.023 relative to the Planck 2018 CMB power spectra bestfit ΛCDM model andA _{lens}= 1.005 ± 0.023 relative to the ACT DR4 + WMAP bestfit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination of ${S}_{8}^{\mathrm{CMBL}}\equiv {\sigma}_{8}{\left({\mathrm{\Omega}}_{m}/0.3\right)}^{0.25}$ from ACT DR6 CMB lensing alone and ${S}_{8}^{\mathrm{CMBL}}=0.818\pm 0.022$ when combining ACT DR6 and Planck ${S}_{8}^{\mathrm{CMBL}}=0.813\pm 0.018$NPIPE CMB lensing power spectra. These results are in excellent agreement with ΛCDM model constraints from Planck or ACT DR4 + WMAP CMB power spectrum measurements. Our lensing measurements from redshiftsz ∼ 0.5–5 are thus fully consistent with ΛCDM structure growth predictions based on CMB anisotropies probing primarilyz ∼ 1100. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts. 
We measured the crosscorrelation between galaxy weak lensing data from the Kilo Degree Survey (KiDS1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the Planck Legacy survey. We used two samples of source galaxies, selected with photometric redshifts, (0.1 < z B < 1.2) and (1.2 < z B < 2), which produce a combined detection significance of the CMB lensing and weak galaxy lensing crossspectrum of 7.7 σ . With the lower redshift galaxy sample, for which the crosscorrelation was detected at a significance of 5.3 σ , we present joint cosmological constraints on the matter density parameter, Ω m , and the matter fluctuation amplitude parameter, σ 8 , marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration as well as the intrinsic alignment of galaxies. We find our measurement to be consistent with the bestfitting flat ΛCDM cosmological models from both Planck and KiDS1000. We demonstrate the capacity of CMB weak lensing crosscorrelations to set constraints on either the redshift or shear calibration by analysing a previously unused highredshift KiDS galaxy sample (1.2 < z B < 2), with the crosscorrelation detected at a significance of 7 σ . This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.more » « less