The Lyα forest flux correlation function: a perturbation theory perspective

The Ly alpha forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Ly alpha forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the 'renormalization' of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics.

Automated summary

The Lyα forest is a valuable tool for mapping large-scale structures at high redshifts and constraining the distance-redshift relation. By expanding the large-scale correlations in the Lyα forest as cumulants of the optical depth field and relating it to the density field through bias expansion, a direct connection between observable and matter fluctuation statistics is established. Small-scale physics influences predictions, velocity bias origins, and renormalization of large-scale bias coefficients, with both isotropic and anisotropic contributions receiving input from small-scale physics.