Noise estimates for measurements of weak lensing from the Ly α forest

Lensing changes the apparent separation between pixels in the Ly alpha forest of separate quasars or high-redshift objects by changing their observed positions on the sky. This changes the implied correlations in the absorption and in particular makes the Ly alpha forest correlation function, or power spectrum, locally anisotropic in the plane of the sky. We have proposed a method for measuring weak lensing using this effect. Here, we estimate the noise expected in weak lensing maps and power spectra for different sets of observational parameters. We find that surveys of the size and quality of the ones being done today and ones planned for the future will be able to measure the lensing power spectrum at a source redshift of z similar or equal to 2.5 with high precision and even be able to image the distribution of foreground matter with high fidelity on degree scales. For example, we predict that Ly alpha forest lensing measurements from the DESI and WEAVE surveys should yield the mass fluctuation amplitude with a statistical error of similar to 3 per cent, eBOSS similar to 6 per cent. and the proposed MSE survey less than 1 per cent. By dividing the redshift range into multiple bins, some tomographic lensing information should be accessible as well. This would allow for cosmological lensing measurements at higher redshift than are accessible with galaxy shear surveys and correspondingly better constraints on the evolution of dark energy at relatively early times.