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

TL;DR

This paper introduces a general framework for modeling cyclic spacetimes with singularity scattering maps, providing a unified approach to bouncing cosmologies in string theory and loop quantum cosmology, with a focus on covariant and ultralocal conditions.

Contribution

It proposes a novel, general notion of junction conditions for quiescent singularities and characterizes all covariant, ultralocal scattering maps, unifying various bouncing cosmology models.

Findings

Characterized all covariant, ultralocal scattering maps.

Established restrictions on bouncing cosmology scenarios.

Developed a local existence theory for cyclic spacetimes.

Abstract

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