We study the importance of gravitational lensing in modelling the number counts of galaxies for the first time in spectroscopic surveys. We confirm previous results for photometric surveys, showing that lensing cannot be neglected in a survey like LSST since it would infer a significant shift of standard cosmological parameters. For a spectroscopic survey like SKA2, we find that neglecting lensing in the monopole, quadrupole and hexadecapole of the correlation function can also induce an important shift of cosmological parameters. For ΛCDM parameters, the shift is moderate, of the order of 0.6σ or less. However, for a model-independent analysis, that measures the growth rate of structure in each redshift bins, neglecting lensing introduces a shift of up to 2.3σ at high redshift. Since the growth rate is directly used to test the theory of gravity, such a strong shift would wrongly be interpreted as the breakdown of General Relativity. This shows the importance of including lensing in the analysis of future surveys. For a survey like DESI, we find on the other hand that lensing is not important, mainly due to the value of the magnification bias parameter of DESI, s(z), which strongly reduces the lensing contribution at high redshift. This result relies on our theoretical modelling of s(z) in DESI and should therefore be confirmed with measurements of s(z) in simulations. We also propose a way of improving the analysis of spectroscopic surveys, by including the cross-correlations between different redshift bins (which is neglected in spectroscopic surveys) from the spectroscopic survey or from a different photometric sample. We show that including the cross-correlations in the SKA2 analysis does not improve the constraints. On the other hand replacing the cross-correlations from SKA2 by cross-correlations measured with LSST improves the constraints by 10% to 20%. The marginal improvement is mainly due to the density correlations between nearby bins and, therefore, does not strongly depend on our knowledge of the magnification bias. Interestingly, for standard cosmological parameter estimation, the photometric survey LSST in its 12 redshift bin configuration and the spectroscopic SKA2 survey are highly complementary, since they are affected by different degeneracies between parameters: LSST yields the tightest constraints on Ωcdm, h and n s, while SKA2 better constrains Ωbaryon, A s and the bias.

Abstract We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards from the observer to the emitters, we solve the Sachs optical equations and study in detail the weak-lensing convergence, ellipticity and rotation. For the first time, we apply such an analysis to a high-resolution relativistic N-body simulation, which consistently includes the leading-order corrections due to general relativity on both large and small scales. These are related to the question of gauge choice and to post-Newtonian corrections, respectively. We present the angular power spectra and one-point probability distribution functions for the weak-lensing variables, which we find are broadly in agreement with comparable Newtonian simulations. Our geometric approach, however, is more robust and flexible, and can therefore be applied consistently to non-standard cosmologies and modified theories of gravity.

Clustering of a perfect fluid does not lead to the generation of vorticity. It is the collisionless nature of dark matter, inducing velocity dispersion and shell crossing, which is at the origin of cosmological vorticity generation. In this paper we investigate the generation of vorticity during the formation of cosmological large scale structure using the public relativistic N-body code gevolution. We test several methods to compute the vorticity power spectrum and we study its convergence with respect to the mass and grid resolution of our simulations. We determine the power spectrum, the spectral index on large-scales, the amplitude of the peak position and their time evolution. We also compare the vorticity extracted from our simulations with the vector perturbations of the metric. Our results are accompanied by resolution studies and compared with previous studies in the literature.