The evolution of large-scale structures within the standard model of cosmology is well posed only up to the onset of shell crossing, where particle trajectories appear to intersect. Beyond this point, the evolution equations become nonpredictive and perturbative approaches break down. We show that in general relativity, a matter horizon forms before caustics develop for a well-defined initial overdensity on an expanding Friedmann–Lemaître–Robertson–Walker spacetime. The matter horizon was first identified by Ellis and Stoeger in 2010 as a dynamical causal boundary that encloses a subregion of spacetime where structure formation actually takes place. We construct a multiscale hierarchical framework for the propagation of the geodesic congruences that avoids the shell-crossing singularity by cutting the spacetime at the matter horizon and gluing to another spacetime with opposite orientation. We identify a relationship between the multiscale hierarchical framework and the cosmological zoom-in N-body simulation approach, and relate the local subregion that decoupled from the Hubble flow to the region of interest in the cosmological zoom-in N-body simulation approach. Most importantly, the multiscale hierarchical framework provides a more robust way of implementing the boundary conditions, which could benefit the cosmological zoom-in N-body simulation approach.

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• Evolution of the Universe
• Large scale structure of the Universe
• Relativistic aspects of cosmology