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General Relativistic effects on the clustering of matter in the universeprovide a sensitive probe of cosmology and gravity theories that can be testedwith the upcoming generation of galaxy surveys. Here, we present a suite oflarge volume high-resolution N-body simulations specifically designed togenerate light-cone data for the study of relativistic effects onlensing-matter observables. RayGalGroupSims (or in short RayGal) consists oftwo N-body simulations of $(2625\,h^{-1}\,{\rm Mpc})^3$ volume with $4096^3$particles of a standard flat $\Lambda$CDM model and a non-standard $w$CDMphantom dark energy model. Light-cone data from the simulations have beengenerated using a parallel ray-tracing algorithm that has accurately solvedbillion geodesic equations. Catalogues and maps with relativistic weak-lensingwhich include post-Born effects, magnification bias (MB) and redshift spacedistortions (RSD) due to gravitational redshift, Doppler, transverse Doppler,Integrated Sachs-Wolfe/Rees-Sciama effects, are publicly released. Using thisdataset, we are able to reproduce the linear and quasi-linear predictions fromthe Class relativistic code for the 10 (cross-)power spectra (3$\times$2points) of the matter density fluctuation field and the gravitationalconvergence at $z=0.7$ and $z=1.8$. We find $1-30\%$ level contribution fromboth MB and RSD to the matter power spectrum, while the Fingers-of-God effectis visible at lower redshift in the non-linear regime. MB contributes at the$10-30\%$ level to the convergence power spectrum leading to a deviationbetween the shear power-spectrum and the convergence power-spectrum. MB alsoplays a significant role in the galaxy-galaxy lensing by decreasing thedensity-convergence spectra by $20\%$, while coupling non-trivialconfigurations (such as the one with the convergence at the same or even lowerredshift than the density field).

The RayGalGroupSims cosmological simulation suite for the study of relativistic effects: an application to lensing-matter clustering statistics