On General-Relativistic Lagrangian Perturbation Theory and Its Non-Perturbative Generalization

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 an 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 an exact average model, Ricci-flat LTB models. The 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.