Photo-z optimization for measurements of the BAO radial direction
  Baryon Acoustic Oscillations (BAO) in the radial direction offer a method to directly measure the Universe expansion history, and to set limits to space curvature when combined to the angular BAO signal. In addition to spectroscopic surveys, radial BAO might be measured from accurate enough photometric redshifts obtained with narrow-band filters. We explore the requirements for a photometric survey using Luminous Red Galaxies (LRG) to competitively measure the radial BAO signal and discuss the possible systematic errors of this approach. If LRG were a highly homogeneous population, we show that the photo-z accuracy would not substantially improve by increasing the number of filters beyond $\sim 10$, except for a small fraction of the sources detected at high signal-to-noise, and broad-band filters would suffice to achieve the target $\sigma_z = 0.003 (1+z)$ for measuring radial BAO. Using the LRG spectra obtained from SDSS, we find that the spectral variability of LRG substantially worsens the achievable photometric redshift errors, and that the optimal system consists of $\sim$ 30 filters of width $\Delta \lambda / \lambda \sim 0.02$. A $S/N > 20$ is generally necessary at the filters on the red side of the $H\alpha$ break to reach the target photometric accuracy. We estimate that a 5-year survey in a dedicated telescope with etendue in excess of 60 ${\rm m}^2 {\rm deg}^2$ would be necessary to obtain a high enough density of galaxies to measure radial BAO with sufficiently low shot noise up to $z= 0.85$. We conclude that spectroscopic surveys have a superior performance than photometric ones for measuring BAO in the radial direction. 
Daniel Roig, Licia Verde, Jordi Miralda-Escude, Raul Jimenez, Carlos   Pena-Garay