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

TL;DR

This paper theoretically estimates the potential to detect cross-correlation between Lyman-alpha flux fluctuations and CMB lensing, which could reveal insights into large-scale structure growth at high redshifts.

Contribution

It introduces a new observable, the Lyman-alpha flux and CMB lensing cross-correlation, and assesses its detectability using linear theory and signal-to-noise estimates.

Findings

Estimated total S/N of 9 with SDSS-III and Planck

Estimated total S/N of 20 with future CMB experiments

Detection would measure neutral hydrogen-matter cross-correlation

Abstract

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 SDSS-III with Planck and of 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.