Non-linear matter clustering in cosmology

Establish a consistent framework for modelling matter clustering on non-linear scales in cosmology.

Background

The paper highlights that accurate modelling of matter clustering has historically been restricted to large (linear) scales due to limitations of the point-particle approximation in General Relativity, which leads to singularities. This motivates the need for a consistent approach on non-linear scales where these approximations break down.

The authors propose a multi-scale framework using matched asymptotic expansions and manifold surgery to include spacetime backreaction effects, aiming to address aspects of this long-standing challenge. Nonetheless, they explicitly state that modelling on non-linear scales remains an open problem in cosmology.