We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg 2 of griz imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric-redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while "blind" to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat ΛCDM and wCDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for ΛCDM) or 7 (for wCDM) cosmological parameters including the neutrino mass density and including the 457 × 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions and from their combination obtain S 8 ≡ σ 8 ðΩ m =0.3Þ 0.5 ¼ 0.773 þ0.026 −0.020 and Ω m ¼ 0.267 þ0.030 −0.017 for ΛCDM; for wCDM, we find S 8 ¼ 0.782 þ0.036 −0.024 , Ω m ¼ 0.284 þ0.033 −0.030 , and w ¼ −0.82 þ0.21 −0.20 at 68% C.L. The precision of these DES Y1 constraints rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for S 8 and Ω m are lower than the central values from Planck for both ΛCDM and wCDM, the Bayes factor indicates that the DES Y1 and Planck data sets are consistent with each other in the context of ΛCDM. Combining DES Y1 with Planck, baryonic acoustic oscillation measurements from SDSS, 6dF, and BOSS and type Ia supernovae from the Joint Lightcurve Analysis data set, we derive very tight constraints on cosmological parameters: S 8 ¼ 0.802 AE 0.012 and Ω m ¼ 0.298 AE 0.007 in ΛCDM and w ¼ −1.00 þ0.05 −0.04 in wCDM. Upcoming Dark Energy Survey analyses will provide more stringent tests of the ΛCDM model and extensions such as a time-varying equation of state of dark energy or modified gravity.

This work and its companion paper, Amon et al. [Phys. Rev. D 105, 023514 (2022)], present cosmic shear measurements and cosmological constraints from over 100 million source galaxies in the Dark Energy Survey (DES) Year 3 data. We constrain the lensing amplitude parameter S 8 ≡ σ 8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω m =0.3 p at the 3% level in ΛCDM: S 8 ¼ 0.759 þ0.025 −0.023 (68% CL). Our constraint is at the 2% level when using angular scale cuts that are optimized for the ΛCDM analysis: S 8 ¼ 0.772 þ0.018 −0.017 (68% CL). With cosmic shear alone, we †

In many cosmological inference problems, the likelihood (the probability of the observed data as a function of the unknown parameters) is unknown or intractable. This necessitates approximations and assumptions, which can lead to incorrect inference of cosmological parameters, including the nature of dark matter and dark energy, or create artificial model tensions. Likelihood-free inference covers a novel family of methods to rigorously estimate posterior distributions of parameters using forward modelling of mock data. We present likelihood-free cosmological parameter inference using weak lensing maps from the Dark Energy Survey (DES) SV data, using neural data compression of weak lensing map summary statistics. We explore combinations of the power spectra, peak counts, and neural compressed summaries of the lensing mass map using deep convolution neural networks. We demonstrate methods to validate the inference process, for both the data modelling and the probability density estimation steps. Likelihood-free inference provides a robust and scalable alternative for rigorous large-scale cosmological inference with galaxy survey data (for DES, Euclid and LSST). We have made our simulated lensing maps publicly available.