On the cosmic previrialization
Abstract
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 F3(k⃗,q⃗,−q⃗) for density, and G3(k⃗,q⃗,−q⃗) for velocity divergence, are clearly non-symmetric under exchange of k⃗ with q⃗. 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 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. The divergent contribution from Pδ22 to the one-loop power spectrum cancels exactly that arising from Pδ13 . Angularly averaged divergence-free part of F3 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 (≃ 1.817 ≤ C ≤ 1.843), for any form of the linear power spectrum.
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BibTeX
@misc{bera2026cosmic,
title = {{On the cosmic previrialization}},
author = {Shubhadip Bera and Michał J. Chodorowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17805},
eprint = {2609.17805},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17805},
}
RIS
TY - UNPB
TI - On the cosmic previrialization
AU - Shubhadip Bera
AU - Michał J. Chodorowski
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.17805
UR - https://arxiv.org/abs/2609.17805
AB - 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(k⃗,q⃗,−q⃗) for density, and G_3(k⃗,q⃗,−q⃗) for velocity divergence, are clearly non-symmetric under exchange of k⃗ with q⃗. 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_δ22 to the one-loop power spectrum cancels exactly that arising from P_δ13 . 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 (≃ 1.817 ≤ C ≤ 1.843), for any form of the linear power spectrum.
ER -