On the importance of lensing for galaxy clustering in photometric and
  spectroscopic surveys
  We study the importance of gravitational lensing in the modelling of the
number counts of galaxies. 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 cosmological parameters. For a spectroscopic
survey like SKA2, we find that neglecting lensing in the monopole, quadrupole
and hexadecapole of the correlation function also induces an important shift of
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 bin, 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. On the other
hand, for a survey like DESI, we find 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. 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 %. Interestingly, for ${\Lambda}$CDM parameters, we
find that LSST and SKA2 are highly complementary, since they are affected
differently by degeneracies between parameters.
