Dynamics of gravitational clustering I. building perturbative expansions

Jul, 2001
13 pages
Published in:
  • Astron.Astrophys. 379 (2001) 8
e-Print:

Citations per year

20012007201320192023012345
Abstract: (arXiv)
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit calculation of the second-order terms which are shown to agree with the results obtained from the hydrodynamical description of the system. Then, we explain that this identity extends to all orders of perturbation theory and that the perturbative series actually diverge for hierarchical scenarios. However, since the collisionless Boltzmann equation provides the exact description of the dynamics (including the non-linear regime) these results may serve as a basis for a study of the non-linear regime. In particular, we derive a non-perturbative quadratic integral equation which explicitly relates the actual non-linear distribution function to the initial conditions (more precisely, to the linear growing mode). This allows us to write an explicit path-integral expression for the probability distribution of the exact non-linear density field.
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