Inferring high redshift large-scale structure dynamics from the
  Lyman-alpha forest
  One of the major science goals over the coming decade is to test fundamental
physics with probes of the cosmic large-scale structure out to high redshift.
Here we present a fully Bayesian approach to infer the three-dimensional cosmic
matter distribution and its dynamics at $z>2$ from observations of the
Lyman-$\alpha$ forest. We demonstrate that the method recovers the unbiased
mass distribution and the correct matter power spectrum at all scales. Our
method infers the three-dimensional density field from a set of one-dimensional
spectra, interpolating the information between the lines of sight. We show that
our algorithm provides unbiased mass profiles of clusters, becoming an
alternative for estimating cluster masses complementary to weak lensing or
X-ray observations. The algorithm employs a Hamiltonian Monte Carlo method to
generate realizations of initial and evolved density fields and the
three-dimensional large-scale flow, revealing the cosmic dynamics at high
redshift. The method correctly handles multi-modal parameter distributions,
which allow constraining the physics of the intergalactic medium (IGM) with
high accuracy. We performed several tests using realistic simulated quasar
spectra to test and validate our method. Our results show that detailed and
physically plausible inference of three-dimensional large-scale structures at
high redshift has become feasible.
