On the cosmic previrialization

RESUMO

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 corresponding variances is crucial for describing the departure from linear structure formation. We calculate the first nonlinear correction to the variance of the cosmic density and velocity fields. 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 forms of the third-order kernels $F_3(\vec{k},\vec{q},-\vec{q})$ for density, and $G_3(\vec{k},\vec{q},-\vec{q})$ for velocity divergence, are clearly non-symmetric under exchange of $\vec{k}$ with $\vec{q}$. However, the calculation of the variance involves a symmetric double integral of these variables, so in this particular case the kernels can be additionally symmetrized. We therefore explicitly symmetrize these kernels $F_3$ and $G_3$, 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. The divergent contribution from $P_{\delta 22}\,$ to the one-loop power spectrum cancels exactly that arising from $P_{\delta 13}$ . Angularly averaged divergence-free part of $F_3$ turns out to be remarkably close to a constant. We found that the corresponding coefficient of the leading-order correction is confined to a remarkably narrow interval of 4007/2205 to 4063/2205 $(\simeq 1.817 \leq C \leq 1.843)$, for any form of the linear power spectrum.