Lenses in the forest: Cross correlation of the lyman-α flux with cosmic microwave background lensing

We present a theoretical estimate for a new observable: the cross correlation between the Lyman-α flux fluctuations in quasar spectra and the convergence of the cosmic microwave background 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-α forest, we estimate a total signal-to-noise of 9 for cross correlating quasar spectra of SDSS-III with Planck and 20 for cross correlating with a future polarization based cosmic microwave background 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.