Cosmic density field reconstruction from Lyα forest data

We present a novel, fast method to recover the density field through the statistics of the transmitted flux in high-redshift quasar absorption spectra. The proposed technique requires the computation of the probability distribution function of the transmitted flux (P_F) in the Lyα forest region and, as a sole assumption, the knowledge of the probability distribution function of the matter density field (P_Δ). We show that the probability density conservation of the flux and matter density unveils a flux-density (F-Δ) relation which can be used to invert the Lyα forest without any assumption on the physical properties of the intergalactic medium. We test our inversion method at z = 3 through the following steps: (i) simulation of a sample of synthetic spectra for which P_Δ is known; (ii) computation of P_F; and (iii) inversion of the Lyα forest through the F-Δ relation. Our technique, when applied to only 10 observed spectra characterized by a signal-to-noise ratio ≥ 100, provides an exquisite (relative error ɛ_Δ≲ 12 per cent in ≳50 per cent of the pixels) reconstruction of the density field in ≳90 per cent of the line of sight. We finally discuss strengths and limitations of the method.