2026/07/23 by Miguel A. Sabogal, Luis A. Escamilla, Davide Pedrotti +2
#astro-ph.CO #gr-qc #hep-ph
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 \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 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.