Lenses in the forest: cross--correlation of the Lyman-alpha flux with CMB lensing

We present a theoretical estimate for a new observable: the cross-correlation between the Lyman-{alpha}-flux fluctuations in quasar (QSO) spectra and the convergence of the cosmic microwave background (CMB) as measured along the same line-of-sight. As a first step toward the assessment of its detectability, we estimate the signal-to-noise ratio using linear theory. Although the signal-to-noise is small for a single line-of-sight and peaks at somewhat smaller redshifts than those probed by the Lyman-{alpha} forest, we estimate a total signal-to-noise of 9 for cross-correlating QSO spectra of SDSSIII with Planck and 20 for cross-correlating with a future polarization based CMB experiment. The detection of this effect would be a direct measure of the neutral hydrogen-matter cross-correlation and could provide important information on the growth of structures at large scales in a redshift range which is still poorly probed by observations.