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.

arXiv comment54 pages. v2: Construction of plane-symmetric cyclic spacetimes moved to arXiv:2106.09666. v3: Version published in JHEP

References in corpus (43)

• The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
• Loop Quantum Cosmology: A Status Report
• Pre-Big-Bang in String Cosmology
• The Pre-Big Bang Scenario in String Cosmology
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Bouncing Universes in String-inspired Gravity
• Classical Black Hole Production in High-Energy Collisions
• On the Generation of a Scale-Invariant Spectrum of Adiabatic Fluctuations in Cosmological Models with a Contracting Phase
• Bouncing Cosmologies: Progress and Problems
• Loop quantum cosmology of Bianchi I models
• Producing a Scale-Invariant Spectrum of Perturbations in a Hagedorn Phase of String Cosmology
• Quiescent cosmological singularities
• Loop Quantum Cosmology: An Overview
• Is loop quantization in cosmology unique?
• Non-perturbative Gravity, Hagedorn Bounce & CMB
• Resolving Cosmological Singularities
• The Matter Bounce Alternative to Inflationary Cosmology
• Singularity Resolution in Loop Quantum Cosmology: A Brief Overview
• Black holes from high-energy beam--beam collisions
• Critical evaluation of common claims in loop quantum cosmology
• Cosmic recall and the scattering picture of Loop Quantum Cosmology
• Pre-big bang bubbles from the gravitational instability of generic string vacua
• Manufacture of Gowdy spacetimes with spikes
• Big Bounce and inhomogeneities
• The loop quantum cosmology bounce as a Kasner transition
• A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
• Regular two-component bouncing cosmologies and perturbations therein
• Stable Big Bang formation for Einstein's equations: The complete sub-critical regime
• Beyond Inflation: A Cyclic Universe Scenario
• The characteristic initial value problem for plane symmetric spacetimes with weak regularity
• The causal boundary of wave-type spacetimes
• Initial Conditions and the Structure of the Singularity in Pre-Big-Bang Cosmology
• The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology ${\mathbb{S}}^3$
• O(d,d)-invariant collapse/inflation from colliding superstring waves
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• On the backward stability of the Schwarzschild black hole singularity
• Self-gravitating fluid flows with Gowdy symmetry near cosmological singularities
• Compensated compactness and corrector stress tensor for the Einstein equations in T2 symmetry
• On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry
• A global conformal extension theorem for perfect fluid Bianchi space-times
• Stable space-like singularity formation for axi-symmetric and polarized near-Schwarzschild black hole interiors
• Universal scattering laws for quiescent bouncing cosmology
• Bianchi I effective dynamics in Quantum Reduced Loop Gravity

Cited by in corpus (3)

• A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
• Non-singular pre-big bang scenarios from all-order ${\alpha }^{\prime }$ corrections
• Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions