Dark energy and curvature from a future baryonic acoustic oscillation survey using the Lyman-αforest

We explore the requirements for a Lyman-a forest survey designed to measure the angular diameter distance and Hubble parameter at 2 ≤ z ≤ 4 using the standard ruler provided by baryonic acoustic oscillations (BAO). The goal would be to obtain a high enough density of sources to probe the three-dimensional density field on the scale of the BAO feature. A percent-level measurement in this redshift range can almost double the Dark Energy Task Force figure of merit, relative to the case with only a similar precision measurement at z ∼ 1, if the Universe is not assumed to be flat. This improvement is greater than the one obtained by doubling the size of the z ∼ 1 survey, with Planck and a weak Sloan Digital Sky Survey-like z = 0.3 BAO measurement assumed in each case. Galaxy BAO surveys at z ∼ 1 may be able to make an effective Lya forest measurement simultaneously at minimal added cost, because the required number density of quasars is relatively small. We discuss the constraining power as a function of area, magnitude limit (density of quasars), resolution, and signal-to-noise of the spectra. For example, a survey covering 2000 sq. deg. and achieving S/N = 1.8 per A at g = 23 ( ∼ 40 quasars per sq. deg.) with an R ≥ 250 spectrograph is sufficient to measure both the radial and transverse oscillation scales to 1.4% from the Lya forest (or better, if fainter magnitudes and possibly Lyman-break galaxies can be used). At fixed integration time and in the sky-noise-dominated limit, a wider, noisier survey is generally more efficient; the only fundamental upper limit on noise being the need to identify a quasar and find a redshift. Because the Lya forest is much closer to linear and generally better understood than galaxies, systematic errors are even less likely to be a problem.