On the cosmic previrialization

Abstract

Context: Non-linear gravitational evolution affects the growth of density and velocity fluctuations and leads to previrialization effects before virialized structures are formed. Therefore, understanding and quantifying the leading nonlinear corrections to the correspond- ing variances is crucial for describing the departure from linear structure formation. Aims: We calculate the first nonlinear correction to the variance of the cosmic density and velocity fields. Methods: We analyze the 1-loop contributions associated with the second and third order perturbative kernels of both the density and velocity-divergence fields. The relevant form of the third-order kernels F3 for density, and G3 for velocity divergence, are clearly non-symmetric under exchange of k with q. However, the calculation of the variance involves a symmetric double integral of these variables, so in this particular case the kernel can be additionally symmetrized. We therefore explicitly symmetrize these kernels F3 and G3, and express them as functions of the two scalar variables: the cosine of the angle between the two wavevectors and a symmetric function of their magnitudes. This representation enables us to identify and isolate the terms which are divergent before performing the angular integration, and to show their cancellation between the second- and third-order terms. Results: The divergent contribution from Pdelta22 to the one-loop power spectrum cancels exactly that arising from Pdelta13. Angularly averaged divergence-free part of F3 turns out to be remarkably close to a constant. Conclusions: The coefficient of the nonlinear correction to the linear variance of the density field is in a narrow range, from 1.817 to 1.843, for any form of the linear power spectrum.