The non-perturbative regime of cosmic structure formation

Abstract

This paper focusses on the barely understood gap between the weakly nonlinear regime of structure formation and the onset of the virialized regime. While the former is accessed through perturbative calculations and the latter through virialization conditions incorporating dynamical stresses that arise in collisionless self-gravitating systems due to velocity dispersion forces, the addressed regime can only be understood through non-perturbative models. We here present an exact Lagrangian integral that provides a tool to access this regime. We derive a transport equation for the peculiar-gravitational field strength and integrate it along comoving trajectories of fluid elements. The so-obtained integral provides an exact expression that solves the longitudinal gravitational field equation in general. We argue that this integral provides a powerful approximation beyond the Lagrangian perturbative regime, and discuss its relation to known approximations, among them Lagrangian perturbation solutions including the Zel'dovich approximation and approximations for adhesive gravitational clustering, including the adhesion approximation. Furthermore, we propose an iteration scheme for a systematic analytical and numerical construction of trajectory fields. The integral may also be employed to improve inverse reconstruction techniques.

Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves

“…This intermediate step already renders the master equation for the perturbations (48) nonlinear in local coordinates due to the presence of the covariant spatial derivatives. Such an iteration may converge to a nonlinear solution after a sufficient number of steps (see, however, [24], and related iteration procedures for the Newtonian problem [20,21]).…”

Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids

“…Models with isotropic pressure can also be considered as phenomenological models for the generally anisotropic pressure originating from the velocity dispersion of dust particles [47][48][49], by taking velocity moments of the collisionless Vlasov equation [24,25]. For a sequence of modeling assumptions used in nonperturbative extensions of Lagrangian perturbation theory, see the summary [21]. In this paper we will extend relativistic Lagrangian perturbation theory for a dust matter model [L1, L2, L3, L4] to the case of irrotational perfect fluids, and also to cases that are relevant for the modeling of multistream regimes where the dust approximation breaks down.…”

Vlasov–Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory

“…These ansätze unfortunately provide a poor description of the internal structure of collapsed structures. The iterative procedure relying on a transport equation of the gravitational field proposed by Buchert (2006) is potentially one exception, but it was not yet tested against numerical simulations.…”