Guide for the Hubble Tension: Mid-Time Solutions and Generalized PAge Parameterizations
Abstract
In cosmology, the Hubble tension has become one of the most serious challenges in the last decade. Assuming that all the observational data are right, one of the ways out is to modify the standard ΛCDM cosmology. In the literature, the theoretical modifications are mainly made in the early and the late/local universes. But on both sides, some no-go arguments have been proposed recently. In particular, the general no-go arguments for the late-time modifications are mainly based on the PAge parameterization. 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>zCMB and hence the cosmic microwave background (CMB) can be taken into account, while they are also more accurate at low redshifts. With these GPAge parameterizations, we revisit the Hubble tension by using not only the late-time observations but also the observational data of CMB. We find that the Hubble tension could be alleviated (or even resolved) in GPAges significantly different from the standard ΛCDM cosmology, while they are overwhelmingly preferred over ΛCDM by the observational data in terms of all the information criteria. Surprisingly, we find that the new physics in the mid-time might be the key to resolve the Hubble tension.
Related
- GPAge: a Global Parameterization based on cosmic Age for some unified early-time and late-time solutions to the Hubble tension
- Does the inverse distance ladder rule out late-time solutions to the Hubble tension? A model-independent test using DES-Dovekie supernovae and DESI DR2 BAO
- Parameterizations of the Hubble Constant from the Binned Type Ia Supernova Master Sample: Logarithmic versus Power-law Forms
- The Hubble Tension: A Decade Review
- Revisiting the Hubble tension with an inverse power-law early dark energy
BibTeX
@misc{jia2026guide,
title = {{Guide for the Hubble Tension: Mid-Time Solutions and Generalized PAge Parameterizations}},
author = {Jing-Yi Jia and Da-Chun Qiang and Hao Wei},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28260},
eprint = {2608.28260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28260},
}
RIS
TY - UNPB
TI - Guide for the Hubble Tension: Mid-Time Solutions and Generalized PAge Parameterizations
AU - Jing-Yi Jia
AU - Da-Chun Qiang
AU - Hao Wei
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28260
UR - https://arxiv.org/abs/2608.28260
AB - In cosmology, the Hubble tension has become one of the most serious challenges in the last decade. Assuming that all the observational data are right, one of the ways out is to modify the standard ΛCDM cosmology. In the literature, the theoretical modifications are mainly made in the early and the late/local universes. But on both sides, some no-go arguments have been proposed recently. In particular, the general no-go arguments for the late-time modifications are mainly based on the PAge parameterization. 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_CMB and hence the cosmic microwave background (CMB) can be taken into account, while they are also more accurate at low redshifts. With these GPAge parameterizations, we revisit the Hubble tension by using not only the late-time observations but also the observational data of CMB. We find that the Hubble tension could be alleviated (or even resolved) in GPAges significantly different from the standard ΛCDM cosmology, while they are overwhelmingly preferred over ΛCDM by the observational data in terms of all the information criteria. Surprisingly, we find that the new physics in the mid-time might be the key to resolve the Hubble tension.
ER -