Baryon Acoustic Oscillations (BAO) provide a standard ruler of known physical length, making it a promising probe of the nature of dark energy. The detection of 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 a direct measurement of the Hubble parameter at different redshifts, a more sensitive probe of dark energy. The main goal of this paper is to show that a precision of sigma_z ~0.003(1 + z) is sufficient to measure BAO in the radial direction. This precision can be achieved for bright, red galaxies, by using a filter 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 a practical implementation, a new galaxy survey, PAU, to be carried out with a telescope/camera combination with an etendue of about 20 m^2deg^2, and covering 8000 sq. deg. in the sky in four years. We expect to measure positions and redshifts 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). This population has a number density n > 10^-3 Mpc^-3 h^3 within the 9 (Gpc/h)^3 volume of the survey, ensuring that the error in the determination of the BAO scale is not limited by shot-noise. By itself, such a survey will deliver precisions of order 5% in the dark-energy equation of state parameter w, if assumed constant, and can determine its time derivative when combined with future CMB measurements. In addition, PAU will yield high-quality redshift and low-resolution spectroscopy for hundreds of millions of other galaxies.
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