Hubble tension: the shape wall
Abstract
The standard "no-go theorem" against late-time solutions to the Hubble tension is essentially a normalization wall, since Baryon Acoustic Oscillation (BAO) measurements constrain the product H0rd, with rd the sound horizon at baryon drag. However, late-time solutions (which keep rd fixed) are tightly constrained not only by the BAO normalization H0rd, but also by the shape of the expansion history, i.e. the dimensionless expansion rate E(z) ≡ H(z)/H0. We show that, if rd and the acoustic angular scale θs are fixed, an increase in H0 needs to be matched by an equal fractional increase in the dimensionless distance integral I ≡ ∫ dz/E(z): δH0/H0 ≃ δI/I. We use this to quantify the "shape wall" set by relative distance constraints on E(z), which we reconstruct nonparametrically, using Gaussian Processes and the latest unanchored Type Ia Supernovae (SNeIa) and BAO data. In our most conservative analysis using PantheonPlus SNeIa and DESI DR2 BAO data, we find a maximum fractional increase in H0 of ≲ 2%, falling well short of the ≳ 8% required to solve the tension. This shape wall holds even in the presence of early-time new physics, and limits the maximum increase in H0 which can be contributed by late-time modifications to E(z) at fixed θs. Therefore, late-time modifications, whether invoked alone or alongside early-time new physics, face not only the well-known normalization wall, but also a stringent percent-level shape wall.
Related
- The Hubble Tension: A Decade Review
- Revisiting the Hubble tension with an inverse power-law early dark energy
- Stars Would Remember a Recent Gravitational Transition: Testing G-step Resolutions of the Hubble Tension with Red Dwarfs
- Dark Radiation Sticks Together: Dark QCD and the Hubble Tension
- Resolving the Hubble Tension in the Early Dark Energy Framework with JWST and DESI Data
BibTeX
@misc{sabogal2026hubble,
title = {{Hubble tension: the shape wall}},
author = {Miguel A. Sabogal and Luis A. Escamilla and Davide Pedrotti and Edvig Selimaj and Sunny Vagnozzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.21244},
eprint = {2607.21244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21244},
}
RIS
TY - UNPB
TI - Hubble tension: the shape wall
AU - Miguel A. Sabogal
AU - Luis A. Escamilla
AU - Davide Pedrotti
AU - Edvig Selimaj
AU - Sunny Vagnozzi
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2607.21244
UR - https://arxiv.org/abs/2607.21244
AB - The standard "no-go theorem" against late-time solutions to the Hubble tension is essentially a normalization wall, since Baryon Acoustic Oscillation (BAO) measurements constrain the product H_0r_d, with r_d the sound horizon at baryon drag. However, late-time solutions (which keep r_d fixed) are tightly constrained not only by the BAO normalization H_0r_d, but also by the shape of the expansion history, i.e. the dimensionless expansion rate E(z) ≡ H(z)/H_0. We show that, if r_d and the acoustic angular scale θ_s are fixed, an increase in H_0 needs to be matched by an equal fractional increase in the dimensionless distance integral I ≡ ∫ dz/E(z): δH_0/H_0 ≃ δI/I. We use this to quantify the "shape wall" set by relative distance constraints on E(z), which we reconstruct nonparametrically, using Gaussian Processes and the latest unanchored Type Ia Supernovae (SNeIa) and BAO data. In our most conservative analysis using PantheonPlus SNeIa and DESI DR2 BAO data, we find a maximum fractional increase in H_0 of ≲ 2%, falling well short of the ≳ 8% required to solve the tension. This shape wall holds even in the presence of early-time new physics, and limits the maximum increase in H_0 which can be contributed by late-time modifications to E(z) at fixed θ_s. Therefore, late-time modifications, whether invoked alone or alongside early-time new physics, face not only the well-known normalization wall, but also a stringent percent-level shape wall.
ER -