Hubble tension: the shape wall

Hubble tension: the shape wall
Miguel A. Sabogal, Luis A. Escamilla, Davide Pedrotti, Edvig Selimaj, Sunny Vagnozzi
arXiv:2607.21244v2 Announce Type: replace
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 $H_0r_d$, 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 $E(z) equiv H(z)/H_0$. We show that, if $r_d$ and the acoustic angular scale $theta_s$ are fixed, an increase in $H_0$ needs to be matched by an equal fractional increase in the dimensionless distance integral $I equiv int dz/E(z)$: $delta H_0/H_0 simeq delta I/I$. 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 $lesssim 2%$, falling well short of the $gtrsim 8%$ 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 $theta_s$. 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.arXiv:2607.21244v2 Announce Type: replace
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 $H_0r_d$, 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 $E(z) equiv H(z)/H_0$. We show that, if $r_d$ and the acoustic angular scale $theta_s$ are fixed, an increase in $H_0$ needs to be matched by an equal fractional increase in the dimensionless distance integral $I equiv int dz/E(z)$: $delta H_0/H_0 simeq delta I/I$. 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 $lesssim 2%$, falling well short of the $gtrsim 8%$ 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 $theta_s$. 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.