We present a measurement of the quasar luminosity function in the range 0.68<z<4 down to extinction corrected magnitude g_dered=22.5, using a simple and well understood target selection technique based on the time-variability of quasars. The complete
ness of our sample was derived directly from a control sample of quasars, without requiring complex simulations of quasar light-curves or colors. A total of 1877 quasar spectra were obtained from dedicated programs on the Sloan telescope (as part of the SDSS-III/BOSS survey) and on the Multiple Mirror Telescope. They allowed us to derive the quasar luminosity function. It agrees well with previously published results in the redshift range 0.68<z<2.6. Our deeper data allow us to extend the measurement to z=4. We measured quasar densities to g_dered<22.5, obtaining 30 QSO per deg^2 at z<1, 99 QSO per deg^2 for 1<z<2.15, and 47 QSO per deg^2 at z>2.15. Using pure luminosity evolution models, we fitted our LF measurements, and predicted quasar number counts as a function of redshift and observed magnitude. These predictions are useful inputs for future cosmology surveys such as those relying on the observation of quasars to measure baryon acoustic oscillations.
Among the tools available for the study of the dark energy driving the expansion of the Universe, Baryon Acoustic Oscillations (BAO) and their effects on the matter power spectrum are particularly attractive. It was recently proposed to study these o
scillations by mapping the 21cm emission of the neutral hydrogen in the redshift range $0.5<z<3$. We discuss here the precision of such measurements using radio-interferometers consisting of arrays of dishes or north-south oriented cylinders. We then discuss the resulting uncertainties on the BAO scales and the sensitivity to the parameters of the Dark Energy equation of state.
