arXiv2026
With about 1.5 billion galaxies expected to be observed, the very large number of objects in the Euclid photometric survey will allow for precise studies of galaxy clustering from a single survey, over a large range of redshifts $0.2 < z < 2.5$. In this work, we use photometric redshifts to extract the baryon acoustic oscillation signal (BAO) from the Flagship galaxy mock catalogue with a tomographic approach to constrain the evolution of the Universe and infer its cosmological parameters. We measured the two-point angular correlation function in 13 redshift bins. A template-fitting approach was applied to the measurement to extract the shift of the BAO peak through the transverse Alcock-Paczynski parameter $α$. A joint analysis of all redshift bins was performed to constrain $α$ at the effective redshift $z_\mathrm{eff}=0.77$ with MCMC and profile likelihood techniques. We also extracted one $α_i$ parameter per redshift bin to quantify its evolution as a function of time. From these 13 $α_i$, which are directly proportional to the ratio $D_\mathrm{A}/r_\mathrm{d}$, we constrain the product $h\,r_\mathrm{d}$ and $Ω_\mathrm{m}$. From the joint analysis, we constrain $D_\mathrm{A}/r_\mathrm{d}=10.764^{+0.0839}_{-0.0849}$, a three-fold improvement over current constraints from the Dark Energy Survey. As expected, the constraining power in the analysis of each redshift bin is lower, with an uncertainty ranging from $\pm\,1.23$ to $\pm\,0.289$. From these results, we constrain $Ω_\mathrm{m}=0.296^{+0.074}_{-0.059}$ and $h\,r_\mathrm{d}=99.35^{+4.29}_{-4.55}\,\mathrm{Mpc}$. We quantify the influence of analysis choices such as the template, scale cuts, redshift bins, and systematic effects such as redshift-space distortions, over our constraints, both at the level of the extracted $α_i$ parameters and at the level of cosmological inference.