We use a variety of simulations that account for: errors in source detection and characterization, clustering, and variations in the assumed source model used to simulate sources within the field and characterize source count incompleteness. Using observations over two extragalactic fields (COSMOS and XMM-LSS), we provide a comprehensive investigation into correcting the incompleteness of the raw source counts within the survey to understand the true underlying source count population. We also find that the usual first-order Limber approximation is insufficiently accurate for LSST Year 10 3x2pt analysis on ℓ=200−1000, whereas invoking the second-order Limber approximation on these scales (with a full non-Limber method at smaller ℓ) does suffice.Ībstract: Abstract We present deep 1.4 GHz source counts from ∼5 deg2 of the continuum Early Science data release of the MeerKAT International Gigahertz Tiered Extragalactic Exploration survey down to S1.4GHz ∼15 $\mu$Jy. For this and other reasons discussed herein, alternative approaches such as matter and Levin may be necessary for a full exploration of parameter space. This method, however, requires further development and testing to extend its use to certain analysis scenarios, particularly those involving a scale-dependent growth rate. We find that in the challenge's fiducial 3x2pt LSST Year 10 scenario, FKEM(CosmoLike) produces the fastest run time within the required accuracy by a considerable margin, positioning it favourably for use in Bayesian parameter inference. We quantify the performance, in terms of accuracy and speed, of three non-Limber implementations: FKEM(CosmoLike), Levin, and matter, themselves based on different integration schemes and approximations. In this paper, we present the results of the 'N5K non-Limber integration challenge', the goal of which was to quantify the performance of different approaches to calculating the angular power spectrum of galaxy number counts and cosmic shear data without invoking the so-called 'Limber approximation', in the context of the Rubin Observatory Legacy Survey of Space and Time (LSST). The rapidly increasing statistical power of cosmological imaging surveys requires us to reassess the regime of validity for various approximations that accelerate the calculation of relevant theoretical predictions.
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