We constrain the matter density ωm and the amplitude of density fluctuations σ8 within the ΛCDM cosmological model with shear peak statistics and angular convergence power spectra using mass maps constructed from the first three years of data of the Dark Energy Survey (DES Y3). We use tomographic shear peak statistics, including cross-peaks: peak counts calculated on maps created by taking a harmonic space product of the convergence of two tomographic redshift bins. Our analysis follows a forward-modelling scheme to create a likelihood of these statistics using N-body simulations, using a Gaussian process emulator. We take into account the uncertainty from the remaining, largely unconstrained ΛCDM parameters (ωb, ns, and h). We include the following lensing systematics: multiplicative shear bias, photometric redshift uncertainty, and galaxy intrinsic alignment. Stringent scale cuts are applied to avoid biases from unmodelled baryonic physics. We find that the additional non-Gaussian information leads to a tightening of the constraints on the structure growth parameter yielding S8 σ8√Ωm/0.3=0.797-0.013+0.015 (68 per cent confidence limits), with a precision of 1.8 per cent, an improvement of 38 per cent compared to the angular power spectra only case. The results obtained with the angular power spectra and peak counts are found to be in agreement with each other and no significant difference in S8 is recorded. We find a mild tension of 1.5 σ between our study and the results from Planck 2018, with our analysis yielding a lower S8. Furthermore, we observe that the combination of angular power spectra and tomographic peak counts breaks the degeneracy between galaxy intrinsic alignment AIA and S8, improving cosmological constraints. We run a suite of tests concluding that our results are robust and consistent with the results from other studies using DES Y3 data.
