Thomas Buchert (Lyon): On general-relativistic Lagrangian perturbation theory

The Newtonian Lagrangian perturbation theory is a widely used framework to study structure formation in cosmology. We review a general-relativistic formulation of such a perturbation approach that can be obtained via a simple dictionary from the Newtonian approach. We then spend some time to introduce the concept of spatially averaging the Einstein equations, discuss some properties of the averaged system and compare with its Newtonian counterpart, also summarizing known theorems on integral properties of cosmological models. Following from these considerations, we provide an average model for the general-relativistic Lagrangian perturbation models.
We discuss subcases of exact solutions related to Szekeres Class II and flat LTB models, serving as a motivation to go beyond Lagrangian perturbation theory on a global homogeneous-isotropic background cosmology. We present ongoing work on a new exact-solution controlled approximation that does not involve a global reference background – a genuine property of general relativity – and it contains Szekeres class I and, on average, non-flat 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.