Limited Impact of CMB B-mode Polarization on Constraints on Cosmic Topology
Abstract
The global spatial structure of the universe is a fundamental question in cosmology. Although the standard model usually assumes a trivial topology, a multiply connected universe can break statistical isotropy and generate off-diagonal covariance between the spherical-harmonic coefficients of cosmic microwave background fluctuations. In this work, we investigate whether CMB B-mode polarization improves constraints on the cubic three-torus, or E1 topology. We construct the full harmonic-space covariance matrices of the temperature, E-mode, and primordial B-mode anisotropies, including correlations between different (ℓ,m) modes, and evaluate Gaussian likelihoods using random realizations generated from a statistically isotropic ΛCDM model with trivial topology. To isolate the intrinsic topological information carried by each CMB observable, we consider the ideal cosmic-variance-limited case, neglecting instrumental noise and gravitational lensing. We find that adding primordial B-mode polarization yields only a marginal improvement in the ability to distinguish the E1 topology from the trivial topology, even under these ideal conditions. The different constraining powers of the temperature, E-mode, and B-mode anisotropies can be understood through the combined effects of their transfer-function responses and the topology-induced off-diagonal correlations in harmonic space. }
Related
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BibTeX
@misc{himeno2026limited,
title = {{Limited Impact of CMB B-mode Polarization on Constraints on Cosmic Topology}},
author = {Ryota Himeno and Atsushi J. Nishizawa and Kiyotomo Ichiki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05960},
eprint = {2610.05960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05960},
}
RIS
TY - UNPB
TI - Limited Impact of CMB B-mode Polarization on Constraints on Cosmic Topology
AU - Ryota Himeno
AU - Atsushi J. Nishizawa
AU - Kiyotomo Ichiki
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.05960
UR - https://arxiv.org/abs/2610.05960
AB - The global spatial structure of the universe is a fundamental question in cosmology. Although the standard model usually assumes a trivial topology, a multiply connected universe can break statistical isotropy and generate off-diagonal covariance between the spherical-harmonic coefficients of cosmic microwave background fluctuations. In this work, we investigate whether CMB B-mode polarization improves constraints on the cubic three-torus, or E_1 topology. We construct the full harmonic-space covariance matrices of the temperature, E-mode, and primordial B-mode anisotropies, including correlations between different (ℓ,m) modes, and evaluate Gaussian likelihoods using random realizations generated from a statistically isotropic ΛCDM model with trivial topology. To isolate the intrinsic topological information carried by each CMB observable, we consider the ideal cosmic-variance-limited case, neglecting instrumental noise and gravitational lensing. We find that adding primordial B-mode polarization yields only a marginal improvement in the ability to distinguish the E_1 topology from the trivial topology, even under these ideal conditions. The different constraining powers of the temperature, E-mode, and B-mode anisotropies can be understood through the combined effects of their transfer-function responses and the topology-induced off-diagonal correlations in harmonic space. }
ER -