ELUCID - Exploring the Local Universe with reConstructed Initial Density
  field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh
  Dynamics
  Simulating the evolution of the local universe is important for studying
galaxies and the intergalactic medium in a way free of cosmic variance. Here we
present a method to reconstruct the initial linear density field from an input
non-linear density field, employing the Hamiltonian Markov Chain Monte Carlo
(HMC) algorithm combined with Particle Mesh (PM) dynamics. The HMC+PM method is
applied to cosmological simulations, and the reconstructed linear density
fields are then evolved to the present day with N-body simulations. The
constrained simulations so obtained accurately reproduce both the amplitudes
and phases of the input simulations at various $z$. Using a PM model with a
grid cell size of 0.75 Mpc/h and 40 time-steps in the HMC can recover more than
half of the phase information down to a scale k~0.85 h/Mpc at high z and to
k~3.4 h/Mpc at z=0, which represents a significant improvement over similar
reconstruction models in the literature, and indicates that our model can
reconstruct the formation histories of cosmic structures over a large dynamical
range. Adopting PM models with higher spatial and temporal resolutions yields
even better reconstructions, suggesting that our method is limited more by the
availability of computer resource than by principle. Dynamic models of
structure evolution adopted in many earlier investigations can induce
non-Gaussianity in the reconstructed linear density field, which in turn can
cause large systematic deviations in the predicted halo mass function. Such
deviations are greatly reduced or absent in our reconstruction.
