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This study demonstrates that late-time cosmological solutions to the Hubble tension face a "shape wall" constraint in addition to the known normalization wall. Using nonparametric analysis of supernova and baryon acoustic oscillation data, the researchers show that keeping early universe parameters fixed allows at most a 2% increase in the Hubble constant H₀, far short of the 8% needed to resolve the tension between early and late universe measurements. The constraint arises because the shape of the cosmic expansion history E(z) is tightly bound by relative distance measurements, limiting how much late-time physics modifications can alter H₀.
Why it matters
This finding significantly narrows the viable paths for resolving the Hubble tension, one of the most pressing problems in modern cosmology. It indicates that solutions likely require modifications to early universe physics rather than late-time cosmological changes, redirecting research efforts in theoretical cosmology and fundamental physics.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
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.
Source: Hubble tension: the shape wall