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.
The SDSS-III BOSS Quasar survey will attempt to observe z>2.15 quasars at a density of at least 15 per square degree to yield the first measurement of the Baryon Acoustic Oscillations in the Ly-alpha forest. To help reaching this goal, we have develo
ped a method to identify quasars based on their variability in the u g r i z optical bands. The method has been applied to the selection of quasar targets in the SDSS region known as Stripe 82 (the Southern equatorial stripe), where numerous photometric observations are available over a 10-year baseline. This area was observed by BOSS during September and October 2010. Only 8% of the objects selected via variability are not quasars, while 90% of the previously identified high-redshift quasar population is recovered. The method allows for a significant increase in the z>2.15 quasar density over previous strategies based on optical (ugriz) colors, achieving a density of 24.0 deg^{-2} on average down to g~22 over the 220 deg^2 area of Stripe 82. We applied this method to simulated data from the Palomar Transient Factory and from Pan-STARRS, and showed that even with data that have sparser time sampling than what is available in Stripe 82, including variability in future quasar selection strategies would lead to increased target selection efficiency in the z>2.15 redshift range. We also found that Broad Absorption Line quasars are preferentially present in a variability than in a color selection.
