Simulating structure formation of the Local Universe

In this work, we present cosmological N-body simulations of the Local Universe with initial conditions constrained by the 2MASS Redshift Survey (2MRS) within a cubic volume of 180 h(-1) Mpc side-length centred at the Local Group. We use a self-consistent Bayesian-based approach to explore the joint parameter space of primordial density fluctuations and peculiar velocity fields, which are compatible with the 2MRS galaxy distribution after cosmic evolution. This method (the kigen code) includes the novel augmented Lagrangian perturbation theory (LPT) structure formation model which combines second-order LPT (2LPT) on large scales with the spherical collapse model on small scales. Furthermore, we describe coherent flows with 2LPT and include a dispersion term to model fingers of god (fogs) arising from virialized structures. These implementations are crucial to avoid artificial parallel filamentary structures, which appear when using the structure formation model with the 2LPT approximation and the data with compressed fogs. We assume Lambda CDM cosmology throughout our method. The recovered initial Gaussian fields are used to perform a set of 25 constrained simulations. Statistically, this ensemble of simulations is in agreement with a reference set of 25 simulations based on randomly seeded Gaussian fluctuations in terms of matter statistics, power spectra and mass functions. Considering the entire volume of (180 h(-1) Mpc)(3), we obtain correlation coefficients of about 98.3 per cent for the cell-to-cell comparison between the simulated density fields and the galaxy density field in log space with Gaussian smoothing scales of r(S) = 3.5 h(-1) Mpc (74 per cent for r(S) = 1.4 h(-1) Mpc). The cross power spectra show correlations with the galaxy distribution which weakens towards smaller length-scales until they vanish at scales of 2.2-3.0 h(-1) Mpc. The simulations we present provide a fully non-linear density and velocity field with a high level of correlation with the observed galaxy distribution at scales of a few Mpc.