BAO+BBN revisited -- Growing the Hubble tension with a 0.7km/s/Mpc constraint

The combination of Baryonic Acoustic Oscillation (BAO) data together with light element abundance measurements from Big Bang Nucleosynthesis (BBN) has been shown to constrain the cosmological expansion history to an unprecedented degree. Using the newest LUNA data and DR16 data from SDSS, the BAO+BBN probe puts tight constraints on the Hubble parameter ($H_0 = 67.6 \pm 1.0 \mathrm{km/s/Mpc}$), resulting in a $3.7\sigma$ tension with the local distance ladder determination from SH0ES in a $\Lambda$CDM model. In the updated BAO data the high- and low-redshift subsets are mutually in excellent agreement, and there is no longer a mild internal tension to artificially enhance the constraints. Adding the recently-developed ShapeFit analysis yields $H_0 = 68.3 \pm 0.7 \mathrm{km/s/Mpc}$ ($3.8 \sigma$ tension). For combinations with additional data sets, there is a strong synergy with the sound horizon information of the cosmic microwave background, which leads to one of the tightest constraints to date, $H_0 = 68.30\pm 0.45\mathrm{km/s/Mpc}$, in $4.2\sigma$ tension with SH0ES. The region preferred by this combination is perfectly in agreement with that preferred by ShapeFit. The addition of supernova data also yields a $4.2\sigma$ tension with SH0ES for Pantheon, and a $3.5\sigma$ tension for PantheonPLUS. Finally, we show that there is a degree of model-dependence of the BAO+BBN constraints with respect to early-time solutions of the Hubble tension, and the loss of constraining power in extended models depends on whether the model can be additionally constrained from BBN observations.