Causal Horizons, Geodesic Completeness and Stability in Slow Contraction Cosmology
Abstract
We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, slow contraction admits a stable past attractor asymptoting to Minkowski space, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde,Guth and Vilenkin theorem and are past geodesically complete. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.
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BibTeX
@misc{khaldieh2026causal,
title = {{Causal Horizons, Geodesic Completeness and Stability in Slow Contraction Cosmology}},
author = {Mariam Khaldieh and Anna I. Rosenzweig and Paul J. Steinhardt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.07815},
eprint = {2607.07815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07815},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Causal Horizons, Geodesic Completeness and Stability in Slow Contraction Cosmology
AU - Mariam Khaldieh
AU - Anna I. Rosenzweig
AU - Paul J. Steinhardt
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2607.07815
UR - https://arxiv.org/abs/2607.07815
AB - We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, slow contraction admits a stable past attractor asymptoting to Minkowski space, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde,Guth and Vilenkin theorem and are past geodesically complete. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.
ER -