# Cosmic distance determination from photometric redshift samples using BAO peaks only

## TL;DR

This paper introduces a wedge approach to extract cosmic distance information from photometric galaxy samples despite redshift uncertainties, achieving about 6% precision in measuring the angular diameter distance.

## Contribution

The study proposes a novel wedge analysis method to recover cosmic distance information from photometric redshift samples, overcoming redshift measurement uncertainties.

## Key findings

- Performs accurate measurement of angular diameter distance D_A from photometric samples.
- Radial distance H^{-1} remains unmeasurable with photometric uncertainties.
- Achieves ~6% precision in D_A measurement, comparable to spectroscopic surveys.

## Abstract

The galaxy distributions along the line-of-sight are significantly contaminated by the uncertainty on redshift measurements obtained through multiband photometry, which makes it difficult to get cosmic distance information measured from baryon acoustic oscillations, or growth functions probed by redshift distortions. We investigate the propagation of the uncertainties into large scale clustering by exploiting all known estimators, and propose the wedge approach as a promising analysis tool to extract cosmic distance information still remaining in the photometric galaxy samples. We test our method using simulated galaxy maps with photometric uncertainties of $\sigma_{0} =\left(0.01, 0.02, 0.03\right)$. The measured anisotropy correlation function $\xi$ is binned into the radial direction of $s$ and the angular direction of $\mu$, and the variations of $\xi(s,\mu)$ with perpendicular and radial cosmic distance measures of $D_A$ and $H^{-1}$ are theoretically estimated by an improved RSD model. Although the radial cosmic distance $H^{-1}$ is unable to be probed from any of the three photometric galaxy samples, the perpendicular component of $D_A$ is verified to be accurately measured even after the full marginalisation of $H^{-1}$. We measure $D_A$ with approximately 6% precision which is nearly equivalent to what we can expect from spectroscopic DR12 CMASS galaxy samples.