While the standard model of cosmology fits most cosmological observations to extraordinary accuracy, some tensions between the model and observations seem to persist despite the increasing quality of data.
Although these tensions might be related to systematic effects, they can also be the first signs of new physics. New insights into these open questions can come from the analysis of the non-linear matter distribution. For this reason, the next generation of surveys will map the galaxy distribution out to z~3. However, future surveys will be limited by survey systematic effects. To address this problem, I will present a new data model that is insensitive to survey systematics and provides unbiased results from data subject to unknown contaminations. Complementary to galaxies, the Lyman-alpha forest traces the under-dense regions of the Universe with very high resolution. By tracing scales down to a few Mpc, the Lyman-alpha forest is sensitive to neutrino masses and dark matter models. In this talk, I will present a Bayesian framework to infer the matter distribution and its dynamics at z>2 from the Lyman-alpha forest.
This method provides the dark matter density and velocity fields as well as unbiased cluster and void profiles.