On The Importance Of Lensing For Galaxy Clustering In Photometric And Spectroscopic Surveys

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 Lambda CDM parameters, the shift is moderate, of the order of 0.6 sigma 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 2.3 sigma 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 Omega(cdm), h and n(s), while SKA2 better constrains Omega(baryon), A(s) and the bias.