A new method to determine $H_0$ from cosmological energy-density measurements

We introduce a new method for measuring the Hubble parameter from low-redshift large-scale observations that is independent of the comoving sound horizon. The method uses the baryon-to-photon ratio determined by the primordial deuterium abundance, together with Big Bang Nucleosynthesis (BBN) calculations and the present-day CMB temperature to determine the physical baryon density $\Omega_b h^2$. The baryon fraction $\Omega_b/\Omega_m$ is measured using the relative amplitude of the baryonic signature in galaxy clustering measured by the Baryon Oscillation Spectroscopic Survey, scaling the physical baryon density to the physical matter density. The physical density $\Omega_mh^2$ is then compared with the geometrical density $\Omega_m$ from Alcock-Paczynski measurements from Baryon Acoustic Oscillations (BAO) and voids, to give $H_0$. Including type Ia supernovae and uncalibrated BAO, we measure $H_0 = 67.1^{+6.3}_{-5.3}$ km s$^{-1}$ Mpc$^{-1}$. We find similar results when varying analysis choices, such as measuring the baryon signature from the reconstructed correlation function, or excluding supernovae or voids. This measurement is currently consistent with both the distance-ladder and CMB $H_0$ determinations, but near-future large-scale structure surveys will obtain 3--4$\times$ tighter constraints.