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with their photometric redshifts obtained together with ground-based observations. This large dataset, with well controlled systematic effects,
will allow for cosmological analyses using the angular clustering of galaxies (GCph) and cosmic shear (WL). For Euclid these two cosmological
probes will not be independent because they will probe the same volume of the Universe. The cross-correlation (XC) between these probes can
tighten constraints and it is therefore important to quantify their impact for Euclid.
Aims. In this study we therefore extend the recent Euclid forecasts presented in Euclid Collaboration: Blanchard et al. (2019) by carefully quantifying
the impact of XC not only on the final parameter constraints for different cosmological models, but also on the nuisance parameters. In
particular, we aim at understanding the amount of additional information that XC can provide for parameters encoding systematic effects, such as
galaxy bias, intrinsic alignments (IA), or the knowledge of the redshift distributions.
Methods. We follow the Fisher matrix formalism presented in Euclid Collaboration: Blanchard et al. (2019) and make use of the codes validated
therein.We also investigate a different galaxy bias model, obtained from the Flagship simulation, and additional photometric-redshift uncertainties,
and the impact of including the XC terms in constraining these.
Results. Starting with a baseline model, we show that the XC terms reduce the uncertainties on galaxy bias by ~ 17% and the uncertainties on IA
by a factor ~ 4. The XC terms also help in constraining the parameter for minimal modified gravity models. Concerning galaxy bias, we observe
that the role of the XC terms on the final parameter constraints is qualitatively the same irrespective of the specific galaxy bias model used. For IA
we show that the XC terms can help in distinguishing between different models, and that if IA terms are neglected then this can lead to significant
biases on the cosmological parameters. Finally, we show that the XC terms can lead to a better determination of the mean of the photometric
Conclusions.We find that the XC between GCph and WL within the Euclid survey is necessary to extract the full information content from the data
in future analyses. These terms help in better constraining the cosmological model, and also lead to a better understanding of the systematic effects
that contaminate these probes. Furthermore, we find that XC significantly helps in constraining the mean of the photometric-redshift distributions,
but, at the same time, it requires a more precise knowledge of this mean, with respect to single probes, in order not to degrade the final FoM.