Cosmic shear cosmology beyond two-point statistics: a combined peak count and correlation function analysis of DES-Y1

We constrain cosmological parameters from a joint cosmic shear analysis of peak-counts and the two-point shear correlation functions, as measured from the Dark Energy Survey (DES-Y1). We find thestructure growth parameter S8≡σ8√Ωm/0.3=0.766+0.033−0.038, which at 4.8% precision, provides one ofthe tightest constraints onS8from the DES-Y1 weak lensing data. In our simulation-based method wedetermine the expected DES-Y1 peak-count signal for a range of cosmologies sampled in four wCDMparameters (Ωm,σ8,h,w0). We also determine the joint covariance matrix with over 1000 realisationsat our fiducial cosmology. With mock DES-Y1 data we calibrate the impact of photometric redshiftand shear calibration uncertainty on the peak-count, marginalising over these uncertainties in our cos-mological analysis. Using dedicated training samples we show that our measurements are unaffectedby mass resolution limits in the simulation, and that our constraints are robust against uncertaintyin the effect of baryon feedback. Accurate modelling for the impact of intrinsic alignments on thetomographic peak-count remains a challenge, currently limiting our exploitation of cross-correlatedpeak counts between high and low redshift bins. We demonstrate that once calibrated, a fully tomo-graphic joint peak-count and correlation functions analysis has the potential to reach a 3% precisiononS8for DES-Y1. Our methodology can be adopted to model any statistic that is sensitive to thenon-Gaussian information encoded in the shear field. In order to accelerate the development of thesebeyond-two-point cosmic shear studies, our simulations are made available to the community upon request.