tokens: and lower values of , respectively. 3.4. Constraining H<sub>0</sub> with BAO plus Deuterium Abundance in ΛCDM Obtaining a constraint on H 0 from the BAO requires adding information to break the degeneracy. One way to do this is to add a constraint on the baryon density (e.g., Addison et al. 2013 ; Aubourg et al. 2015 ; Wang et al. 2017 ). We assume that the photon energy density, or, equivalently, the CMB mean temperature, is also known. The CMB temperature was measured precisely by COBE /FIRAS (Fixsen et al. 1996 ; Fixsen 2009 ) and we view this result as independent of the CMB anisotropy measurements performed by more recent experiments. Note that while the H 0 in the H ( z ) in the denominator of (1) cancels in the product, some residual H 0 dependence still exists because the decoupling redshift and the sound speed depend on the physical matter and radiation densities, and , respectively, while the expansion rate H ( z ) depends on the fractional densities and . In the BAO fit with an external baryon density prior, performs double duty. It not only goes into determining the late-time expansion ( D M and H at the BAO survey redshifts) but also controls the expansion history in the early universe prior to baryons decoupling from photons, since the photon and neutrino properties (with ) are held fixed. As well as providing an indirect H 0 constraint, the BAO+ fit also serves as something of a self-consistency test of early and late-time expansion. The most precise constraints on independent of the CMB power spectrum come from estimates of the primordial deuterium abundance. In standard Big Bang nucleosynthesis (BBN), the abundance of light nuclei is determined by a single parameter, the baryon-to-photon ratio η (see recent review by Cyburt et al. 2016 , and references therein). Taking the photon number density as fixed from the CMB temperature, a measurement of the primordial deuterium abundance in conjunction with knowledge of BBN physics provides a constraint on . Precise estimates of the primordial deuterium abundance have been made in recent years using extremely metal-poor damped Ly α (DLA) systems along sight lines to high-redshift quasars (e.g., Pettini Cooke 2012 ; Cooke et al. 2014 , 2016 ; Riemer-Sørensen et al. 2017 ). Cooke et al. ( 2016 ; hereafter C16 ) reportby combining six such systems. The reaction rate plays a key role in the conversion from D/H to . Using the theoretical calculation for this rate from Marcucci et al. ( 2016 ), C16 findwhich is lower than the Planck value (assuming a standard model throughout). Using instead an empirically derived rate, C16 findwhich has a larger uncertainty but is in better agreement with CMB-derived values. We performed fits to the galaxy-plus-Ly α BAO data with the addition of each of the Gaussian priors on in ( 6 ) and ( 7 ) in turn. We show parameter constraints in Table 3 , including the WMAP 9-year and Planck 2016 CMB anisotropy constraints for comparison. Table 3 Constraints
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