ELUCID - Exploring the Local Universe with reConstructed Initial Density field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh Dynamics

Abstract

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.