Clustering with general photo-$z$ uncertainties: Application to Baryon Acoustic Oscillations

Understand

Photometric data can be analyzed using the three-dimensional correlation function $\xi_{\rm p}$ to extract cosmological information via e.g., measurement of the Baryon Acoustic Oscillations (BAO).

• Previous studies modeled $\xi_{\rm p} $ assuming a Gaussian photo-$z$ approximation.
• In this work we improve the modeling by incorporating realistic photo-$z$ distribution.
• We show that the position of the BAO scale in $\xi_{\rm p}$ is determined by the photo-$z$ distribution and the Jacobian of the transformation.