Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation

Abstract

We develop a new nonlinear method to model structure formation in general relativity from a generalization of the relativistic Lagrangian perturbation schemes, controlled by Szekeres (and LTB) exact solutions. The overall approach can be interpreted as the evolution of a deformation field on an inhomogeneous reference model, obeying locally Friedmann-like equations. In the special case of locally one-dimensional deformations, the new model contains the entire Szekeres family of exact solutions. As thus formulated, this approach paraphrases the Newtonian and relativistic Zel'dovich approximations, having a large potential for applications in contexts where relativistic degrees of freedom are relevant. Numerical simulations are implemented to illustrate the capabilities and accuracy of the model.

21 pages, 4 figures, matches published version in PRD

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Cited by in corpus (4)

• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood
• Direct correspondence between Newtonian gravitation and general relativity
• An effective $\mathbf{\Lambda }$-Szekeres modelling of the local Universe with Cosmicflows-4