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We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of $1289{\mathrm{deg}}^2$. With the combined measurements from four source galaxy redshift bins, we obtain a detection significance of $5.8\sigma$. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial $\mathrm{\Lambda }\mathrm{CDM}$ model, finding $A=0.99\pm 0.17$. We additionally use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Finally, when performing a cosmological analysis under the $\mathrm{\Lambda }\mathrm{CDM}$ model, we obtain the marginalized constraints of ${\mathrm{\Omega }}_{\mathrm{m}}=0.261_{-0.051}^{+0.070}$ and $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}/0.3}=0.660_{-0.100}^{+0.085}$. These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT, and Planck data.

We derive cosmological constraints from the probability distribution function (PDF) of evolved large-scale matter density fluctuations. We do this by splitting lines of sight by density based on their count of tracer galaxies, and by measuring both gravitational shear around and counts-in-cells in overdense and underdense lines of sight, in Dark Energy Survey (DES) First Year and Sloan Digital Sky Survey (SDSS) data. Our analysis uses a perturbation theory model [O. Friedrich et al., Phys. Rev. D 98, 023508 (2018)] and is validated using $N$-body simulation realizations and log-normal mocks. It allows us to constrain cosmology, bias and stochasticity of galaxies with respect to matter density and, in addition, the skewness of the matter density field. From a Bayesian model comparison, we find that the data weakly prefer a connection of galaxies and matter that is stochastic beyond Poisson fluctuations on $\le 20\mathrm{arcmin}$ angular smoothing scale. The two stochasticity models we fit yield DES constraints on the matter density ${\mathrm{\Omega }}_m=0.26_{-0.03}^{+0.04}$ and ${\mathrm{\Omega }}_m=0.28_{-0.04}^{+0.05}$ that are consistent with each other. These values also agree with the DES analysis of galaxy and shear two-point functions (3x2pt, DES Collaboration et al.) that only uses second moments of the PDF. Constraints on ${\sigma }_8$ are model dependent (${\sigma }_8=0.97_{-0.06}^{+0.07}$ and $0.80_{-0.07}^{+0.06}$ for the two stochasticity models), but consistent with each other and with the 3 x 2pt results if stochasticity is at the low end of the posterior range. As an additional test of gravity, counts and lensing in cells allow to compare the skewness $S_3$ of the matter density PDF to its $\mathrm{\Lambda }\mathrm{CDM}$ prediction. We find no evidence of excess skewness in any model or data set, with better than 25 per cent relative precision in the skewness estimate from DES alone.

We present density split statistics, a framework that studies lensing and counts-in-cells as a function of foreground galaxy density, thereby providing a large-scale measurement of both 2-point and 3-point statistics. Our method extends our earlier work on trough lensing and is summarized as follows: given a foreground (low redshift) population of galaxies, we divide the sky into subareas of equal size but distinct galaxy density. We then measure lensing around uniformly spaced points separately in each of these subareas, as well as counts-in-cells statistics (CiC). The lensing signals trace the matter density contrast around regions of fixed galaxy density. Through the CiC measurements this can be related to the density profile around regions of fixed matter density. Together, these measurements constitute a powerful probe of cosmology, the skewness of the density field and the connection of galaxies and matter. In this paper we show how to model both the density split lensing signal and CiC from basic ingredients: a non-linear power spectrum, clustering hierarchy coefficients from perturbation theory and a parametric model for galaxy bias and shot-noise. Using N-body simulations, we demonstrate that this model is sufficiently accurate for a cosmological analysis on year 1 data from the Dark Energy Survey.

We present a measurement of the angular baryon acoustic oscillation (BAO) scale from the completed Dark Energy Survey (DES) dataset excluding the area of overlap with the Dark Energy Spectroscopic Instrument (DESI). We follow the same methodology and validation process as in the DES Y6 BAO analysis. We interpret the impact of this measurement in the context of the statistical preference for “$w_0{w}_a$ cold dark matter (CDM) over $\mathrm{\Lambda }\mathrm{CDM}$ when combined with DES Y5 Type Ia supernovae (SN), Planck CMB, and DESI BAO. Based on our previous work, using the full Y6 DES BAO sample, in combination with SN, CMB and DESI data release 1 (DR1) BAO, added $0.3\sigma$ in this preference (from $3.7\sigma$ to $4.0\sigma$), but this ignored possible correlations between datasets. Using our new DESI-independent DES BAO likelihood instead, we find a smaller increase in the statistical preference for $w_0{w}_a\mathrm{CDM}$, from $3.7\sigma$ to $3.8\sigma$ when using DESI DR1 BAO, and from $4.0\sigma$ to $4.1\sigma$ when updating to the more recent DESI data release 2 (DR2) BAO. These significances reduce to $3.1\sigma$ when using the new calibrated DES SN-Dovekie. Alongside this work, we publicly release baofit_wtheta, the BAO fitting code for the angular correlation function used in the DES Y6 BAO analysis.

The kinematic and thermal Sunyaev-Zel’dovich (kSZ and tSZ) effects probe the abundance and thermodynamics of ionized gas in galaxies and clusters. We present a new hybrid estimator to measure the kSZ effect by combining cosmic microwave background temperature anisotropy maps with photometric and spectroscopic optical survey data. The method interpolates a velocity reconstruction from a spectroscopic catalog at the positions of objects in a photometric catalog, which makes it possible to leverage the high number density of the photometric catalog and the precision of the spectroscopic survey. Combining this hybrid kSZ estimator with a measurement of the tSZ effect simultaneously constrains the density and temperature of free electrons in the photometrically selected galaxies. Using the $1000{\mathrm{deg}}^2$ of overlap between the Atacama Cosmology Telescope (ACT) Data Release 5, the first three years of data from the Dark Energy Survey (DES), and the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we detect the kSZ signal at $4.8\sigma$ and reject the null (no-kSZ) hypothesis at $5.1\sigma$. This corresponds to $2.0\sigma$ per 100,000 photometric objects with a velocity field based on a spectroscopic survey with $1/5^{\mathrm{th}}$ the density of the photometric catalog. For comparison, a recent ACT analysis using exclusively spectroscopic data from BOSS measured the kSZ signal at $2.1\sigma$ per 100,000 objects. Our derived constraints on the thermodynamic properties of the galaxy halos are consistent with previous measurements. With future surveys, such as the Dark Energy Spectroscopic Instrument and the Rubin Observatory Legacy Survey of Space and Time, we expect that this hybrid estimator could result in measurements with significantly better signal-to-noise than those that rely on spectroscopic data alone.

In this paper, we present and validate the galaxy sample used for the analysis of the baryon acoustic oscillation (BAO) signal in the Dark Energy Survey (DES) Y6 data. The definition is based on a color and redshift-dependent magnitude cut optimized to select galaxies at redshifts higher than 0.6, while ensuring a high-quality photo-$z$ determination. The optimization is performed using a Fisher forecast algorithm, finding the optimal $i$-magnitude cut to be given by $i<19.64+2.894z_{\mathrm{ph}}$. For the optimal sample, we forecast an increase in precision in the BAO measurement of $\sim 25\%$ with respect to the Y3 analysis. Our BAO sample has a total of 15,937,556 galaxies in the redshift range $0.6<z_{\mathrm{ph}}<1.2$, and its angular mask covers $4,273.42{\mathrm{deg}}^2$ to a depth of $i=22.5$. We validate its redshift distributions with three different methods: directional neighborhood fitting algorithm (DNF), which is our primary photo-$z$ estimation; direct calibration with spectroscopic redshifts from VIPERS, which is a spectroscopic galaxy sample that overlaps with our BAO sample and is complete within our selection cuts; and clustering redshift using SDSS galaxies. The fiducial redshift distribution is a combination of these three techniques performed by modifying the mean and width of the DNF distributions to match those of VIPERS and clustering redshift. In this paper, we also describe the methodology used to mitigate the effect of observational systematics, which is analogous to the one used in the Y3 analysis. This paper is one of the two dedicated to the analysis of the BAO signal in DES Y6. In its companion paper, we present the angular diameter distance constraints obtained through the fitting to the BAO scale.

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters—focusing on ${\mathrm{\Omega }}_m$—are split into versions associated with structure growth (e.g., ${\mathrm{\Omega }}_m^{\mathrm{grow}}$) and expansion history (e.g., ${\mathrm{\Omega }}_m^{\mathrm{geo}}$). Once the parameters have been specified for the $\mathrm{\Lambda }\mathrm{CDM}$ cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves both as a (largely) model-independent test for beyond-$\mathrm{\Lambda }\mathrm{CDM}$ physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multiprobe DES data as [Phys. Rev. Lett. 122, 171301 (2019)] : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}$. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure ${\mathrm{\Omega }}_m^{\mathrm{grow}}$, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parametrization where we split both ${\mathrm{\Omega }}_m$ and $w$, but find that even our most constraining data combination is unable to separately constrain ${\mathrm{\Omega }}_m^{\mathrm{grow}}$ and $w^{\mathrm{grow}}$. Relative to $\mathrm{\Lambda }\mathrm{CDM}$, splitting growth and geometry weakens bounds on ${\sigma }_8$ but does not alter constraints on $h$.

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel’dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range 0.25–1.78 over a total sky area of $5200{\mathrm{deg}}^2$. We use DES Year 3 weak-lensing data for 688 clusters with redshifts $z<0.95$ and HST weak-lensing data for 39 clusters with $0.6<z<1.7$. The weak-lensing measurements enable robust mass measurements of sample clusters and allow us to empirically constrain the SZ observable-mass relation without having to make strong assumptions about, e.g., the hydrodynamical state of the clusters. For a flat $\mathrm{\Lambda }\mathrm{CDM}$ cosmology, and marginalizing over the sum of massive neutrinos, we measure ${\mathrm{\Omega }}_{\mathrm{m}}=0.286\pm 0.032$, ${\sigma }_8=0.817\pm 0.026$, and the parameter combination ${\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.25}=0.805\pm 0.016$. Our measurement of $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}/0.3}=0.795\pm 0.029$ and the constraint from Planck CMB anisotropies (2018 TT, TE, $\mathrm{EE}+\mathrm{lowE}$) differ by $1.1\sigma$. In combination with that Planck dataset, we place a 95% upper limit on the sum of neutrino masses $\sum m_{\nu }<0.18\mathrm{eV}$. When additionally allowing the dark energy equation of state parameter $w$ to vary, we obtain $w=-1.45\pm 0.31$ from our cluster-based analysis. In combination with Planck data, we measure $w=-1.34_{-0.15}^{+0.22}$, or a $2.2\sigma$ difference with a cosmological constant. We use the cluster abundance to measure ${\sigma }_8$ in five redshift bins between 0.25 and 1.8, and we find the results to be consistent with structure growth as predicted by the $\mathrm{\Lambda }\mathrm{CDM}$ model fit to Planck primary CMB data.

The combination of multiple observational probes has long been advocated as a powerful technique to constrain cosmological parameters, in particular dark energy. The Dark Energy Survey has measured 207 spectroscopically confirmed type Ia supernova light curves, the baryon acoustic oscillation feature, weak gravitational lensing, and galaxy clustering. Here we present combined results from these probes, deriving constraints on the equation of state, $w$, of dark energy and its energy density in the Universe. Independently of other experiments, such as those that measure the cosmic microwave background, the probes from this single photometric survey rule out a Universe with no dark energy, finding $w=-0.80_{-0.11}^{+0.09}$. The geometry is shown to be consistent with a spatially flat Universe, and we obtain a constraint on the baryon density of ${\mathrm{\Omega }}_b=0.069_{-0.012}^{+0.009}$ that is independent of early Universe measurements. These results demonstrate the potential power of large multiprobe photometric surveys and pave the way for order of magnitude advances in our constraints on properties of dark energy and cosmology over the next decade.

We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find ${\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}=0.81\pm 0.06$ (68% confidence), after marginalizing over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About 20% of our error bar comes from marginalizing over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both data sets. Our uncertainties are $\sim 30\%$ larger than those from CFHTLenS when we carry out a comparable analysis of the two data sets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of ${\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}$ is present regardless of the value of $w$.

We perform a joint analysis of the counts and weak lensing signal of redMaPPer clusters selected from the Dark Energy Survey (DES) Year 1 dataset. Our analysis uses the same shear and source photometric redshifts estimates as were used in the DES combined probes analysis. Our analysis results in surprisingly low values for $S_8={\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}=0.65\pm 0.04$, driven by a low matter density parameter, ${\mathrm{\Omega }}_{\mathrm{m}}=0.179_{-0.038}^{+0.031}$, with ${\sigma }_8-{\mathrm{\Omega }}_{\mathrm{m}}$ posteriors in $2.4\sigma$ tension with the DES Y1 3x2pt results, and in $5.6\sigma$ with the Planck CMB analysis. These results include the impact of post-unblinding changes to the analysis, which did not improve the level of consistency with other data sets compared to the results obtained at the unblinding. The fact that multiple cosmological probes (supernovae, baryon acoustic oscillations, cosmic shear, galaxy clustering and CMB anisotropies), and other galaxy cluster analyses all favor significantly higher matter densities suggests the presence of systematic errors in the data or an incomplete modeling of the relevant physics. Cross checks with x-ray and microwave data, as well as independent constraints on the observable-mass relation from Sunyaev-Zeldovich selected clusters, suggest that the discrepancy resides in our modeling of the weak lensing signal rather than the cluster abundance. Repeating our analysis using a higher richness threshold ($\lambda \ge 30$) significantly reduces the tension with other probes, and points to one or more richness-dependent effects not captured by our model.

We perform a joint analysis of the counts of redMaPPer clusters selected from the Dark Energy Survey (DES) year 1 data and multiwavelength follow-up data collected within the $2500{\mathrm{deg}}^2$ South Pole Telescope (SPT) Sunyaev-Zel’dovich (SZ) survey. The SPT follow-up data, calibrating the richness-mass relation of the optically selected redMaPPer catalog, enable the cosmological exploitation of the DES cluster abundance data. To explore possible systematics related to the modeling of projection effects, we consider two calibrations of the observational scatter on richness estimates: a simple Gaussian model which account only for the background contamination (BKG), and a model which further includes contamination and incompleteness due to projection effects (PRJ). Assuming either a $\mathrm{\Lambda }\mathrm{CDM}+\sum m_{\nu }$ or $w\mathrm{CDM}+\sum m_{\nu }$ cosmology, and for both scatter models, we derive cosmological constraints consistent with multiple cosmological probes of the low and high redshift Universe, and in particular with the SPT cluster abundance data. This result demonstrates that the DES Y1 and SPT cluster counts provide consistent cosmological constraints, if the same mass calibration data set is adopted. It thus supports the conclusion of the DES Y1 cluster cosmology analysis which interprets the tension observed with other cosmological probes in terms of systematics affecting the stacked weak lensing analysis of optically selected low–richness clusters. Finally, we analyze the first combined optically SZ selected cluster catalog obtained by including the SPT sample above the maximum redshift probed by the DES Y1 redMaPPer sample ($z=0.65$). Besides providing a mild improvement of the cosmological constraints, this data combination serves as a stricter test of our scatter models: the PRJ model, providing scaling relations consistent between the two abundance and multiwavelength follow-up data, is favored over the BKG model.

We study a phenomenological class of models where dark matter converts to dark radiation in the low redshift epoch. This class of models, dubbed DMDR, characterizes the evolution of comoving dark-matter density with two extra parameters, and may be able to help alleviate the observed discrepancies between early and late-time probes of the Universe. We investigate how the conversion affects key cosmological observables such as the cosmic microwave background (CMB) temperature and matter power spectra. Combining 3x2pt data from Year 1 of the Dark Energy Survey, Planck-2018 CMB temperature and polarization data, supernovae (SN) Type Ia data from Pantheon, and baryon acoustic oscillation (BAO) data from BOSS DR12, MGS and 6dFGS, we place new constraints on the amount of dark matter that has converted to dark radiation and the rate of this conversion. The fraction of the dark matter that has converted since the beginning of the Universe in units of the current amount of dark matter, $\zeta$, is constrained at 68% confidence level to be $<0.32$ for DES-Y1 3x2pt data, $<0.030$ for $\mathrm{CMB}+\mathrm{SN}+\mathrm{BAO}$ data, and $<0.037$ for the combined dataset. The probability that the DES and CMB+SN+BAO datasets are concordant increases from 4% for the $\mathrm{\Lambda }\mathrm{CDM}$ model to 8% (less tension) for DMDR. The tension in $S_8={\sigma }_8\sqrt{{\mathrm{\Omega }}_m/0.3}$ between DES-Y1 3x2pt and $\mathrm{CMB}+\mathrm{SN}+\mathrm{BAO}$ is slightly reduced from $2.3\sigma$ to $1.9\sigma$. We find no reduction in the Hubble tension when the combined data is compared to distance-ladder measurements in the DMDR model. The maximum-posterior goodness-of-fit statistics of DMDR and $\mathrm{\Lambda }\mathrm{CDM}$ model are comparable, indicating no preference for the DMDR cosmology over $\mathrm{\Lambda }\mathrm{CDM}$.

We infer the mean optical depth of a sample of optically selected galaxy clusters from the Dark Energy Survey via the pairwise kinematic Sunyaev-Zel’dovich (KSZ) effect. The pairwise KSZ signal between pairs of clusters drawn from the Dark Energy Survey Year-3 cluster catalog is detected at $4.1\sigma$ in cosmic microwave background temperature maps from two years of observations with the SPT-3G camera on the South Pole Telescope. After cuts, there are 24,580 clusters in the $\sim 1,400{\mathrm{deg}}^2$ of the southern sky observed by both experiments. We infer the mean optical depth of the cluster sample with two techniques. The optical depth inferred from the pairwise KSZ signal is ${\overline{\tau }}_e=(2.97\pm 0.73)\times {10}^{-3}$, while that inferred from the thermal SZ signal is ${\overline{\tau }}_e=(2.51\pm 0.55^{\mathrm{stat}}\pm 0.15^{\mathrm{syst}})\times {10}^{-3}$. The two measures agree at $0.6\sigma$. We perform a suite of systematic checks to test the robustness of the analysis.

The Dark Energy Survey (DES) recently released the final results of its two principal probes of the expansion history: Type Ia supernovae (SNe) and baryonic acoustic oscillations (BAO). In this paper, we explore the cosmological implications of these data in combination with external cosmic microwave background (CMB), big bang nucleosynthesis (BBN), and age-of-the-Universe information. The BAO measurement, which is $\sim 2\sigma$ away from Planck ’s $\mathrm{\Lambda }\mathrm{CDM}$ predictions, pushes for low values of ${\mathrm{\Omega }}_{\mathrm{m}}$ compared to Planck, in contrast to SN which prefers a higher value than Planck. We identify several tensions among datasets in the $\mathrm{\Lambda }\mathrm{CDM}$ model that cannot be resolved by including either curvature ($k\mathrm{\Lambda }\mathrm{CDM}$) or a constant dark energy equation of state ($w\mathrm{CDM}$). By combining $\mathrm{BAO}+\mathrm{SN}+\mathrm{CMB}$ despite these mild tensions, we obtain ${\mathrm{\Omega }}_k=-{5.5}_{-4.2}^{+4.6}\times {10}^{-3}$ in $k\mathrm{\Lambda }\mathrm{CDM}$, and $w=-0.948_{-0.027}^{+0.028}$ in $w\mathrm{CDM}$. In $w\mathrm{CDM}$, BAO and SN push again in different directions of parameter space, favoring, respectively, $w<-1$ and $w>-1$. If we open the parameter space to $w_0{w}_a\mathrm{CDM}$ [where the equation of state of dark energy varies as $w(a)=w_0+(1-a)w_a$], all the datasets are mutually more compatible, and we find concordance in the $[w_0>-1,w_a<0]$ quadrant, with BAO pushing for $w_a<0$ and SN for $[w_0>-1,w_a<0]$. For DES BAO and SN in combination with Planck -CMB, we find a $3.2\sigma$ deviation from $\mathrm{\Lambda }\mathrm{CDM}$, with $w_0=-0.673_{-0.097}^{+0.098}$, $w_a=-1.37_{-0.50}^{+0.51}$, a Hubble constant of $H_0=67.81_{-0.86}^{+0.96}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, and an abundance of matter of ${\mathrm{\Omega }}_{\mathrm{m}}=0.3109_{-0.0099}^{+0.0086}$. For the combination of all the background cosmological probes considered (including CMB’s angular acoustic scale ${\theta }_{\star }$), we still find a deviation of $2.8\sigma$ from $\mathrm{\Lambda }\mathrm{CDM}$ in the $w_0-w_a$ plane. Assuming a minimal neutrino mass, this work provides tentative evidence for non-$\mathrm{\Lambda }\mathrm{CDM}$ physics, which is consistent with recent claims in support of evolving dark energy, or a source of unknown systematics.

Optical imaging surveys measure both the galaxy density and the gravitational lensing-induced shear fields across the sky. Recently, the Dark Energy Survey (DES) Collaboration used a joint fit to two-point correlations between these observables to place tight constraints on cosmology (T. M. C. Abbott et al. (Dark Energy Survey Collaboration), Phys. Rev. D 98, 043526 (2018)). In this work, we develop the methodology to extend the DES Year 1 joint probes analysis to include cross-correlations of the optical survey observables with gravitational lensing of the cosmic microwave background as measured by the South Pole Telescope (SPT) and Planck. Using simulated analyses, we show how the resulting set of five two-point functions increases the robustness of the cosmological constraints to systematic errors in galaxy lensing shear calibration. Additionally, we show that contamination of the SPT+Planck cosmic microwave background lensing map by the thermal Sunyaev-Zel’dovich effect is a potentially large source of systematic error for two-point function analyses but show that it can be reduced to acceptable levels in our analysis by masking clusters of galaxies and imposing angular scale cuts on the two-point functions. The methodology developed here will be applied to the analysis of data from the DES, the SPT, and Planck in a companion work.

We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey (DES) and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel’dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat $\mathrm{\Lambda }\mathrm{CDM}$ cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}/0.3}=0.782_{-0.025}^{+0.019}$ and ${\mathrm{\Omega }}_{\mathrm{m}}=0.260_{-0.019}^{+0.029}$. We test for consistency between these five correlation function measurements and the Planck-only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat $\mathrm{\Lambda }\mathrm{CDM}$ models. Combining constraints from all six two-point functions yields $S_8=0.776_{-0.021}^{+0.014}$ and ${\mathrm{\Omega }}_{\mathrm{m}}=0.271_{-0.016}^{+0.022}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.

We present a tomographic measurement of the cross-correlation between thermal Sunyaev-Zel’dovich (TSZ) maps from Planck and the Atacama Cosmology Telescope and weak galaxy lensing shears measured during the first three years of observations of the Dark Energy Survey. This correlation is sensitive to the thermal energy in baryons over a wide redshift range and is therefore a powerful probe of astrophysical feedback. We detect the correlation at a statistical significance of $21\sigma$, the highest significance to date. We examine the TSZ maps for potential contaminants, including cosmic infrared background and radio sources, finding that cosmic infrared background has a substantial impact on our measurements and must be taken into account in our analysis. We use the cross-correlation measurements to test different feedback models. In particular, we model the TSZ using several different pressure profile models calibrated against hydrodynamical simulations. Our analysis marginalizes over redshift uncertainties, shear calibration biases, and intrinsic alignment effects. We also marginalize over ${\mathrm{\Omega }}_{\mathrm{m}}$ and ${\sigma }_8$ using Planck or DES priors. We find that the data prefer the model with a low amplitude of the pressure profile at small scales, compatible with a scenario with strong active galactic nuclei feedback and ejection of gas from the inner part of the halos. When using a more flexible model for the shear profile, constraints are weaker, and the data cannot discriminate between different baryonic prescriptions.

Cross-correlations of galaxy positions and galaxy shears with maps of gravitational lensing of the cosmic microwave background (CMB) are sensitive to the distribution of large-scale structure in the Universe. Such cross-correlations are also expected to be immune to some of the systematic effects that complicate correlation measurements internal to galaxy surveys. We present measurements and modeling of the cross-correlations between galaxy positions and galaxy lensing measured in the first three years of data from the Dark Energy Survey with CMB lensing maps derived from a combination of data from the $2500{\mathrm{deg}}^2$ SPT-SZ survey conducted with the South Pole Telescope and full-sky data from the Planck satellite. The CMB lensing maps used in this analysis have been constructed in a way that minimizes biases from the thermal Sunyaev Zel’dovich effect, making them well suited for cross-correlation studies. The total signal-to-noise of the cross-correlation measurements is 23.9 (25.7) when using a choice of angular scales optimized for a linear (nonlinear) galaxy bias model. We use the cross-correlation measurements to obtain constraints on cosmological parameters. For our fiducial galaxy sample, which consist of four bins of magnitude-selected galaxies, we find constraints of ${\mathrm{\Omega }}_{\mathrm{m}}={0.272}_{-0.052}^{+0.032}$ and $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}/0.3}={0.736}_{-0.028}^{+0.032}$ (${\mathrm{\Omega }}_{\mathrm{m}}={0.245}_{-0.044}^{+0.026}$ and $S_8={0.734}_{-0.028}^{+0.035}$) when assuming linear (nonlinear) galaxy bias in our modeling. Considering only the cross-correlation of galaxy shear with CMB lensing, we find ${\mathrm{\Omega }}_{\mathrm{m}}={0.270}_{-0.061}^{+0.043}$ and $S_8={0.740}_{-0.029}^{+0.034}$. Our constraints on $S_8$ are consistent with recent cosmic shear measurements, but lower than the values preferred by primary CMB measurements from Planck.

Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulation-based analysis of a set of Gaussian and non-Gaussian weak lensing statistics using detailed mock catalogs of the Dark Energy Survey (DES). We implement: 1) second and third moments; 2) wavelet phase harmonics (WPH); 3) the scattering transform (ST). Our analysis is fully based on simulations, it spans a space of seven $\nu w\mathrm{CDM}$ cosmological parameters, and it forward models the most relevant sources of systematics of the data (masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration). We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a likelihood-free-inference approach. We validate the pipeline extensively, and we find that WPH exhibits the strongest performance when combined with second moments, followed by ST, and then by third moments. The combination of all the different statistics further enhances constraints with respect to second moments, up to 25 percent, 15 percent, and 90 percent for $S_8$, ${\mathrm{\Omega }}_{\mathrm{m}}$, and the figure-of-merit ${\mathrm{FoM}}_{{\mathrm{S}}_8,{\mathrm{\Omega }}_{\mathrm{m}}}$, respectively. We further find that non-Gaussian statistics improve constraints on $w$ and on the amplitude of intrinsic alignment with respect to second moments constraints. The methodological advances presented here are suitable for application to Stage IV surveys from Euclid, Rubin-LSST, and Roman with additional validation on mock catalogs for each survey. In a companion paper we present an application to DES Year 3 data.