Dark energy and curvature from a future baryonic acoustic oscillation   survey using the Lyman-alpha forest
  We explore the requirements for a Lyman-alpha forest (LyaF) 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 SDSS-like z=0.3 BAO measurement assumed in each case. Galaxy BAO surveys at z~1 may be able to make an effective LyaF 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 Ang. 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 LyaF (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 LyaF is much closer to linear and generally better understood than galaxies, systematic errors are even less likely to be a problem. 
Patrick McDonald (CITA) and Daniel Eisenstein (Arizona)