  The angular positions of quasars are deflected by the gravitational lensing
effect of foreground matter. The Lyman-alpha forest seen in the spectra of
these quasars is therefore also lensed. We propose that the signature of weak
gravitational lensing of the forest could be measured using similar techniques
that have been applied to the lensed Cosmic Microwave Background, and which
have also been proposed for application to spectral data from 21cm radio
telescopes. As with 21cm data, the forest has the advantage of spectral
information, potentially yielding many lensed "slices" at different redshifts.
We perform an illustrative idealized test, generating a high resolution angular
grid of quasars (of order arcminute separation), and lensing the
Lyman-alphaforest spectra at redshifts z=2-3 using a foreground density field.
We find that standard quadratic estimators can be used to reconstruct images of
the foreground mass distribution at z~1. There currently exists a wealth of Lya
forest data from quasar and galaxy spectral surveys, with smaller sightline
separations expected in the future. Lyman-alpha forest lensing is sensitive to
the foreground mass distribution at redshifts intermediate between CMB lensing
and galaxy shear, and avoids the difficulties of shape measurement associated
with the latter. With further refinement and application of mass reconstruction
techniques, weak gravitational lensing of the high redshift Lya forest may
become a useful new cosmological probe.
