{"paper":{"title":"Guide for the Hubble Tension: Mid-Time Solutions and Generalized PAge Parameterizations","arxiv_id":"2608.28260","primary_cat":"astro-ph.CO","submitted_at":"2026-08-28T12:24:00+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":"In cosmology, the Hubble tension has become one of the most serious challenges in the last decade.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.01,"quantitative":false,"quantitative_p":0.22,"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":0.98,"id":"s1","own":false,"role":"background","text":"Assuming that all the observational data are right, one of the ways out is to modify the standard $\\Lambda$CDM cosmology.","hedge":{"p":0.8,"label":"hedged_possibility"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.01,"method":0.01,"result":0.0,"background":0.98,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.99,"id":"s2","own":false,"role":"background","text":"In the literature, the theoretical modifications are mainly made in the early and the late/local universes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.01,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.0,"background":0.99,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.82,"id":"s3","own":false,"role":"background","text":"But on both sides, some no-go arguments have been proposed recently.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.17,"method":0.0,"result":0.0,"background":0.82,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.95,"id":"s4","own":false,"role":"background","text":"In particular, the general no-go arguments for the late-time modifications are mainly based on the PAge parameterization.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.04,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.05,"method":0.0,"result":0.0,"background":0.95,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.92,"id":"s5","own":true,"role":"contribution","text":"In the present work, we note that there are some flaws in the (original) PAge parameterization, and then propose various generalized PAge (GPAge) parameterizations, which can be extended to $z>z_{\\rm CMB}$ and hence the cosmic microwave background (CMB) can be taken into account, while they are also more accurate at low redshifts.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.48,"role_probabilities":{"gap":0.0,"method":0.08,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.92,"interpretation":0.0}},{"i":6,"p":0.88,"id":"s6","own":true,"role":"method","text":"With these GPAge parameterizations, we revisit the Hubble tension by using not only the late-time observations but also the observational data of CMB.","hedge":{"p":0.85,"label":"asserted"},"own_p":0.9,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.88,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.12,"interpretation":0.0}},{"i":7,"p":1.0,"id":"s7","own":true,"role":"result","text":"We find that the Hubble tension could be alleviated (or even resolved) in GPAges significantly different from the standard $\\Lambda$CDM cosmology, while they are overwhelmingly preferred over $\\Lambda$CDM by the observational data in terms of all the information criteria.","hedge":{"p":0.52,"label":"hedged_possibility"},"own_p":0.96,"main_claim_p":0.55,"quantitative":true,"quantitative_p":0.74,"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":8,"p":0.8,"id":"s8","own":true,"role":"interpretation","text":"Surprisingly, we find that the new physics in the mid-time might be the key to resolve the Hubble 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