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Baryon Acoustic Oscillations (BAO) provide a standard ruler of known physicallength, making it a promising probe of the nature of dark energy. The detectionof BAO requires measuring galaxy positions and redshifts. "Transversal"(angular distance) BAO measure the angular size of this scale, while"line-of-sight" (or "radial") BAO require precise redshifts, but provide adirect measurement of the Hubble parameter at different redshifts, a moresensitive probe of dark energy. The main goal of this paper is to show that aprecision of sigma_z ~0.003(1 + z) is sufficient to measure BAO in the radialdirection. This precision can be achieved for bright, red galaxies, by using afilter system comprising about 40 filters, each with a width of ~100 A, from ~4000 A to ~ 8000 A, supplemented by two broad-band filters. We describe apractical implementation, a new galaxy survey, PAU, to be carried out with atelescope/camera combination with an etendue of about 20 m^2deg^2, and covering8000 sq. deg. in the sky in four years. We expect to measure positions andredshifts for over 14 million red, early-type galaxies with L > L* and i_AB <22.5 in the interval 0.1 < z < 0.9, with sigma_z < 0.003(1 + z). Thispopulation has a number density n > 10^-3 Mpc^-3 h^3 within the 9 (Gpc/h)^3volume of the survey, ensuring that the error in the determination of the BAOscale is not limited by shot-noise. By itself, such a survey will deliverprecisions of order 5% in the dark-energy equation of state parameter w, ifassumed constant, and can determine its time derivative when combined withfuture CMB measurements. In addition, PAU will yield high-quality redshift andlow-resolution spectroscopy for hundreds of millions of other galaxies.

Measuring Baryon Acoustic Oscillations along the line of sight with photometric redshifs: the PAU survey