Non-Gaussian initial conditions in $\Lambda$CDM: Newtonian, relativistic and primordial contributions

Understand

The goal of the present paper is to set initial conditions for structure formation at non-linear order, consistent with general relativity, while also allowing for primordial non-Gaussianity.

• We use the non-linear continuity and Raychauduri equations, which together with the non-linear 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 $\Lambda$CDM universe, identifying non-linear contributions coming from the Newtonian growing mode, primordial non-Gaussianity and intrinsic non-Gaussianity, due to the essential non-linearity of the relativistic constraint equations.