Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces

For spacetimes containing quiescent singularity hypersurfaces we propose a general notion of junction conditions based on prescribed scattering map, as call it, and introduce the cyclic spacetime (also called multiverse) consisting domains bounded by spacelike or timelike hypersurfaces, across which our map is applied. A local existence theory established here while, in companion paper, construct plane-symmetric spacetimes. We study data space suitably rescaled metric, extrinsic curvature, matter fields can be each side singularity, for class so-called singularities establish restrictions that must satisfy. obtain full characterization all maps are covariant ultralocal, sense define and, particular, distinguish between, one hand, three laws bouncing cosmology universal nature other model-dependent conditions. The proposed this paper applies to without symmetry restriction. It encompasses bouncing-cosmology scenarios, both string loop quantum cosmology, puts strong their possible explicit realizations.