# Weak lensing of the Lyman-alpha forest

## TL;DR

This paper explores the potential of using weak gravitational lensing of the Lyman-alpha forest as a new cosmological probe, demonstrating that quadratic estimators can reconstruct foreground mass distribution from spectral data at high redshifts.

## Contribution

It proposes a novel method to measure weak lensing effects on the Lyman-alpha forest using techniques similar to those applied to CMB and 21cm data, with initial idealized tests showing feasibility.

## Key findings

- Quadratic estimators can reconstruct foreground mass maps from Lyman-alpha forest spectra.
- Lyman-alpha forest lensing probes intermediate redshift structures, complementing CMB and galaxy lensing.
- Potential for future application with extensive spectral survey data.

## Abstract

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.