Abstract　 　　 

    I will talk about our recent work on reconstructing the initial condition of the local universe. We develop a Hamiltonian Markov Chain Monte Carlo method to obtain the linear density field from a posterior probability function that consists of two components: a prior of a Gaussian density field with variances given by the linear power spectrum of the current cold dark matter model and a likelihood term that is given by the current density field. The present-day density field can be reconstructed from galaxy groups using the method developed in Wang et al. Such design can make sure that the reconstructed initial linear density field follows the multivariate Gaussian distribution with the given linear power spectrum and evolves through gravitational instabilities to the present-day density field in the local universe. Using a realistic mock Sloan Digital Sky Survey DR7, obtained by populating dark matter halos in the Millennium simulation (MS) with galaxies, we show that our method can effectively and accurately recover both the amplitudes and phases of the initial, linear density field. To examine the accuracy of our method, we use N-body simulations to evolve these reconstructed initial conditions to the present day. The resimulated density field thus obtained accurately matches the original density field of the MS in the density range 0.3<ρ/ρ_mean<20 without any significant bias. In particular, the Fourier phases of the resimulated density fields are tightly correlated with those of the original simulation down to a scale corresponding to a wavenumber of ∼1 h/Mpc, much smaller than the translinear scale, which corresponds to a wavenumber of ∼0.15 h/Mpc.