On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization

Abstract

The Newtonian Lagrangian perturbation theory is a widely used framework to study structure formation in cosmology in the nonlinear regime. We review a general-relativistic formulation of such a perturbation approach, emphasizing results on already developed extensive formalism including among other aspects: the non-perturbative modeling of Ricci and Weyl curvatures, gravitational waves and pressure-supported fluids. We discuss subcases of exact solutions related to Szekeres Class II and, as exact average model, Ricci-flat LTB models. This latter forms the basis of a generalization that we then propose in terms of a scheme that goes beyond the relativistic Lagrangian perturbation theory on a global homogeneous-isotropic background cosmology. This new approximation does not involve a homogeneous reference background and it contains Szekeres class I (and thus general LTB models) as exact subcases. Most importantly, this new approximation allows for the interaction of structure with an evolving `background cosmology', conceived as a spatial average model, and thus includes cosmological backreaction.

26 pages, 4 figures, matches published version in Universe

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Cited by in corpus (5)

• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood
• Direct correspondence between Newtonian gravitation and general relativity
• Nonperturbative collapse models for collisionless self-gravitating flows
• The averaging problem on the past null cone in inhomogeneous dust cosmologies