{"paper":{"title":"Limited Impact of CMB B-mode Polarization on Constraints on Cosmic Topology","arxiv_id":"2610.05960","primary_cat":"astro-ph.CO","submitted_at":"2026-10-05T08:13:06+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"The global spatial structure of the universe is a fundamental question in cosmology.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.03,"main_claim_p":0.01,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"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.","hedge":{"p":0.63,"label":"hedged_possibility"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.97,"id":"s2","own":true,"role":"contribution","text":"In this work, we investigate whether CMB B-mode polarization improves constraints on the cubic three-torus, or $E_1$ topology.","hedge":{"p":0.64,"label":"unclear"},"own_p":0.5,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.02,"method":0.0,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":true,"role":"method","text":"We construct the full harmonic-space covariance matrices of the temperature, E-mode, and primordial B-mode anisotropies, including correlations between different $(\\ell,m)$ modes, and evaluate Gaussian likelihoods using random realizations generated from a statistically isotropic $\\Lambda$CDM model with trivial topology.","hedge":{"p":0.92,"label":"asserted"},"own_p":0.96,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.99,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":4,"p":0.97,"id":"s4","own":true,"role":"method","text":"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.","hedge":{"p":0.9,"label":"asserted"},"own_p":0.88,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.97,"result":0.0,"background":0.0,"limitation":0.03,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":1.0,"id":"s5","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.95,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"interpretation","text":"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. 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