# Baryon Acoustic Oscillations and the Hubble Constant: Past, Present and Future

## TL;DR

This paper analyzes constraints on the Hubble constant using BAO and BBN data, highlighting current tensions and forecasting future measurement impacts with DESI.

## Contribution

It provides a Bayesian analysis of BAO data tension, measures H0 with current data, and forecasts future constraints considering BBN priors with DESI.

## Key findings

- Current H0 measurement: 67.6±1.1 km/s/Mpc
- Tension between galaxy BAO and Lyman-alpha forest data (~6.3%)
- Future BBN priors significantly affect DESI H0 forecasts

## Abstract

We investigate constraints on the Hubble constant ($H_0$) using Baryon Acoustic Oscillations (BAO) and baryon density measurements from Big Bang Nucleosynthesis (BBN). We start by investigating the tension between galaxy BAO measurements and those using the Lyman-$\alpha$ forest, within a Bayesian framework. Using the latest results from eBOSS DR14 we find that the probability of this tension being statistical is $\simeq6.3\%$ assuming flat $\Lambda$CDM. We measure $H_0 = 67.6\pm1.1$ km s$^{-1}$ Mpc$^{-1}$, with a weak dependence on the BBN prior used, in agreement with results from Planck Cosmic Microwave Background (CMB) results and in strong tension with distance ladder results. Finally, we forecast the future of BAO $+$ BBN measurements of $H_0$, using the Dark Energy Spectroscopic Instrument (DESI). We find that the choice of BBN prior will have a significant impact when considering future BAO measurements from DESI.