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

TL;DR

This paper reviews a general-relativistic Lagrangian perturbation framework for cosmology, extending it non-perturbatively to include complex structures, gravitational waves, and backreaction effects without relying on a homogeneous background.

Contribution

It introduces a novel non-perturbative approximation scheme that generalizes relativistic Lagrangian perturbation theory to include inhomogeneities and backreaction effects without a fixed background.

Findings

Includes non-perturbative modeling of Ricci and Weyl curvatures.

Enables interaction of structure with evolving background cosmology.

Contains Szekeres class I and LTB models as exact cases.

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.