The Lyman-$\alpha$ power spectrum - CMB lensing convergence cross-correlation

Understand

We investigate the three-point correlation between the Lyman-$\alpha$ forest and the CMB weak lensing ($\delta_F \delta_F \kappa$) expressed as the cross-correlation between the CMB weak lensing field and local variations in the forest power spectrum.

• In addition to the standard gravitational bispectrum term, we note the existence of a non-standard systematic term coming from mis-estimation of the mean flux over the finite length of Lyman-$\alpha$ skewers.
• We numerically calculate the angular cross-power spectrum and discuss its features.
• We integrate it into zero-lag correlation function and compare our predictions with recent results by Doux et al..