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

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.

Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions

“…Despite the presence of singularities, we prove that in the generalized setup of 'cyclic spacetimes' proposed in [1,2] we can still prescribe initial data on a hypersurface and solve globally in a suitable sense. While trapped surface are unavoidable only in plane symmetry, they are also a typical phenomenon arising with the Einstein equations even when no symmetry restriction is made [6].…”

“…Causality of singularity scattering maps. The junction conditions were introduced in [2] as relations between suitable rescalings of the scalar field φ, spatial metric g and extrinsic curvature K of a Gaussian foliation on both sides of the singularity. Earlier on, such relations have been proposed in the context of bouncing anisotropic cosmologies that are homogeneous in [12,13]; see also [14,15] for earlier results.…”

“…Plane gravitational waves. We study the gravitational collision problem which we solve beyond singularities in the class of plane-symmetric spacetimes, in a sense that we defined recently in [1,2]. Recall that the global geometry of plane waves (without collisions) was analyzed first by Penrose [3], who emphasized their relevance as an idealization of more general physical phenomena.…”

A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

“…Some physically relevant models require even lower regularity, for instance: spacetimes with conical singularities [94], cosmic strings [93] and (impulsive) gravitational waves (see for instance the pioneering work of Penrose [81], and the more recent [45,Chapt. 20]), or models for cyclic spacetimes [63].…”

A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

“…Some physically relevant models require even lower regularity, for instance: spacetimes with conical singularities [92], cosmic strings [91] and (impulsive) gravitational waves (see for instance the pioneering work of Penrose [80], and the more recent [44,Chapt. 20]), or models for cyclic spacetimes [62].…”