Elucidating $Λ$CDM: Impact of Baryon Acoustic Oscillation Measurements on the Hubble Constant Discrepancy

TL;DR

This paper demonstrates that BAO measurements, when combined with independent CMB data (WMAP, ACTPol, SPT) or with primordial deuterium abundances, favor a lower H0 than the local distance ladder within ΛCDM, independent of Planck. It highlights the importance of using anisotropic BAO information rather than angle-averaged constraints and shows that BAO helps disfavor both the distance-ladder–favored high H0 and the Planck damping-tail–favored low H0. The study also reveals persistent tensions between galaxy and Lyα BAO and explores N_eff variations, concluding that no single dataset reconciles all measurements. Overall, BAO remains a powerful, Planck-independent lever on H0 and the early-universe sound horizon, but the H0 discrepancy persists across multiple probes.

Abstract

We examine the impact of baryon acoustic oscillation (BAO) scale measurements on the discrepancy between the value of the Hubble constant ($H_0$) inferred from the local distance ladder and from Planck cosmic microwave background (CMB) data. While the BAO data alone cannot constrain $H_0$, we show that combining the latest BAO results with WMAP, Atacama Cosmology Telescope (ACT), or South Pole Telescope (SPT) CMB data produces values of $H_0$ that are $2.4-3.1σ$ lower than the distance ladder, independent of Planck, and that this downward pull was less apparent in some earlier analyses that used only angle-averaged BAO scale constraints rather than full anisotropic information. At the same time, the combination of BAO and CMB data also disfavors the lower values of $H_0$ preferred by the Planck high-multipole temperature power spectrum. Combining galaxy and Lyman-$α$ forest (Ly$α$) BAO with a precise estimate of the primordial deuterium abundance produces $H_0=66.98\pm1.18$ km s$^{-1}$ Mpc$^{-1}$ for the flat $Λ$CDM model. This value is completely independent of CMB anisotropy constraints and is $3.0σ$ lower than the latest distance ladder constraint, although $2.4σ$ tension also exists between the galaxy BAO and Ly$α$ BAO. These results show that it is not possible to explain the $H_0$ disagreement solely with a systematic error specific to the Planck data. The fact that tensions remain even after the removal of any single data set makes this intriguing puzzle all the more challenging to resolve.

Figures (3)

• Figure 1: Including BAO data substantially tightens CMB constraints on $H_0$. The observables corresponding to the transverse and line-of-sight BAO scale, $D_M\,r_{d, \textrm{fid.}}/r_d$, and $H\,r_d/r_{d,\textrm{fid.}}$ (Section 2 and Table 1), are shown for redshift $z=0.61$. The blue shaded contours are the measurements from the final BOSS DR12 analysis alam/etal:2017. The different panels contain predictions from different, essentially independent, CMB measurements assuming a flat $\Lambda\mathrm{CDM}$ model, with MCMC samples color-coded by $H_0$ in km s$^{-1}$ Mpc$^{-1}$. The same $\tau=0.07\pm0.02$ prior is used in each case. The addition of the BAO tightens the $H_0$ constraint by more than a factor of three in the case of ACTPol or SPT data (Table 2). When combined with any current CMB data set the galaxy BAO disfavor the values of $H_0$ preferred by the distance ladder riess/etal:2016 at moderate to high significance. The lower values preferred by the high-multipole Planck data (the constraint from the samples shown in the top-right panel is $65.12\pm1.45$ km s$^{-1}$ Mpc$^{-1}$) are also disfavored.
• Figure 3: Left: Comparison of BAO-only constraints in the flat $\Lambda\mathrm{CDM}$ model. Contours containing 68 and 95% of MCMC samples are shown for galaxy ($z_{\rm eff}\leq0.61$) and Ly$\alpha$ forest ($z_{\rm eff}\geq2.3$) BAO separately and in a joint fit using the BAO data listed in Table 1. In flat $\Lambda\mathrm{CDM}$ the late-time expansion rate is determined only by $\Omega_m$, with $H_0r_d$ acting as an overall expansion normalization. Right: Comparison of $\Omega_m$ constraints from BAO, CMB and SNe measurements. The SNe constraint is from the "joint light-curve analysis" (JLA) presented by betoule/etal:2014. While the combined BAO fit produces a tight constraint $\Omega_m=0.293\pm0.020$, in agreement with the CMB and SNe determinations, there is a $2.4\sigma$ tension between the galaxy and Ly$\alpha$ BAO, which individually prefer higher and lower values of $\Omega_m$, respectively.
• Figure 4: Adding an estimate of the baryon density, $\Omega_bh^2$, in this case from deuterium abundance (D/H) measurements, breaks the BAO $H_0-r_d$ degeneracy in $\Lambda\mathrm{CDM}$. The same contours are shown as in Figure 3, with the addition of a Gaussian prior $100\Omega_bh^2=2.156\pm0.020$cooke/etal:2016. In contrast to Figure 3, here $\Omega_m$ determines both the early time expansion, including the absolute sound horizon, $r_d$, as well as the late-time expansion history. The radiation density is fixed from COBE/FIRAS CMB mean temperature measurements. The combined BAO+D/H constraint, $H_0=66.98\pm1.18$ km s$^{-1}$ Mpc$^{-1}$ is $3.0\sigma$ lower than the riess/etal:2016 distance ladder determination and is independent of CMB anisotropy data.