Non-Gaussian initial conditions in ΛCDM: Newtonian, relativistic, and primordial contributions

The goal of the present paper is to set initial conditions for structure formation at nonlinear order, consistent with general relativity, while also allowing for primordial non-Gaussianity. We use the nonlinear continuity and Raychaudhuri equations, which together with the nonlinear energy constraint, determine the evolution of the matter density fluctuation in general relativity. We solve this equations at first and second order in a perturbative expansion, recovering and extending previous results derived in the matter-dominated limit and in the Newtonian regime. We present a second-order solution for the comoving density contrast in a ΛCDM universe, identifying nonlinear contributions coming from the Newtonian growing mode, primordial non-Gaussianity and intrinsic non- Gaussianity, due to the essential nonlinearity of the relativistic constraint equations. We discuss the application of these results to initial conditions in N-body simulations, showing that relativistic corrections mimic a non-zero nonlinear parameter f_NL.