Euclid preparation: XIX. Impact of magnification on photometric galaxy
  clustering
  We investigate the importance of lensing magnification for estimates of
galaxy clustering and its cross-correlation with shear for the photometric
sample of Euclid. Using updated specifications, we study the impact of lensing
magnification on the constraints and the shift in the estimation of the best
fitting cosmological parameters that we expect if this effect is neglected. We
follow the prescriptions of the official Euclid Fisher-matrix forecast for the
photometric galaxy clustering analysis and the combination of photometric
clustering and cosmic shear. The slope of the luminosity function (local count
slope), which regulates the amplitude of the lensing magnification, as well as
the galaxy bias have been estimated from the Euclid Flagship simulation. We
find that magnification significantly affects both the best-fit estimation of
cosmological parameters and the constraints in the galaxy clustering analysis
of the photometric sample. In particular, including magnification in the
analysis reduces the 1$\sigma$ errors on $\Omega_{\text{m},0}, w_{0}, w_a$ at
the level of 20-35\%, depending on how well we will be able to independently
measure the local count slope. In addition, we find that neglecting
magnification in the clustering analysis leads to shifts of up to 1.6$\sigma$
in the best-fit parameters. In the joint analysis of galaxy clustering, cosmic
shear and galaxy-galaxy lensing, including magnification does not improve
precision but it leads to up to 6$\sigma$ bias if neglected. Therefore, for all
models considered in this work, magnification has to be included in the
analysis of galaxy clustering and its cross-correlation with the shear signal
($3\times2$pt analysis) for an accurate parameter estimation.
