Dark energy survey year 3 results: Cosmology from galaxy clustering and galaxy-galaxy lensing in harmonic space

We present the joint tomographic analysis of galaxy-galaxy lensing and galaxy clustering in harmonic space, using galaxy catalogues from the first three years of observations by the Dark Energy Survey (DES Y3). We utilise the redMaGiC and MagLim catalogues as lens galaxies and the METACALIBRATION catalogue as source galaxies. The measurements of angular power spectra are performed using the pseudo-C_ method, and our theoretical modelling follows the fiducial analyses performed by DES Y3 in configuration space, accounting for galaxy bias, intrinsic alignments, magnification bias, shear magnification bias and photometric redshift uncertainties. We explore different approaches for scale cuts based on non-linear galaxy bias and baryonic effects contamination. Our fiducial covariance matrix is computed analytically, accounting for mask geometry in the Gaussian term, and including non-Gaussian contributions and super-sample covariance terms. To validate our harmonic space pipelines and covariance matrix, we used a suite of 1800 log-normal simulations. We also perform a series of stress tests to gauge the robustness of our harmonic space analysis. In the CDM model, the clustering amplitude S₈ =₈ (ₘ/0. 3) ^0. 5 is constrained to S₈ = 0. 704 0. 029 and S₈ = 0. 753 0. 024 (68\% C. L. ) for the redMaGiC and MagLim catalogues, respectively. For the wCDM, the dark energy equation of state is constrained to w = -1. 28 0. 29 and w = -1. 26^+0. 34-₀. ₂₇, for redMaGiC and MagLim catalogues, respectively. These results are compatible with the corresponding DES Y3 results in configuration space and pave the way for harmonic space analyses using the DES Y6 data.