Sound-Horizon-Agnostic Inference of the Hubble Constant and Neutrino Mass from BAO, CMB Lensing, and Galaxy Weak Lensing and Clustering

TL;DR

This work develops a sound-horizon-agnostic approach to infer the Hubble constant by treating the drag epoch sound horizon $r_d$ as a free parameter and combining diverse cosmological probes. By pairing uncalibrated BAO distances (including the CMB acoustic scale via $\theta_{\star}$) with CMB lensing and DES Y3 3×2pt data to constrain $\Omega_m h^2$, the method breaks the $r_d$–$H_0$ degeneracy and yields $H_0 = 70.0 \pm 1.7$ km s$^{-1}$ Mpc$^{-1}$ when $\Sigma m_\nu=0.06$ eV, and $H_0 = 70.03 \pm 0.97$ km s$^{-1}$ Mpc$^{-1}$ with an $A_s$ prior. Allowing $\Sigma m_\nu$ to vary introduces substantial prior dependence and higher $H_0$ values, though a logarithmic prior on $\Sigma m_\nu$ mitigates bias. Forecasts with future CMB lensing (Simons Observatory–like), expanded $3\times2$-pt data, DESI BAO, and SN datasets project sub-percent precision on $H_0$ for fixed $\Sigma m_\nu$ ($\sigma(H_0) \approx 0.67$ km s$^{-1}$ Mpc$^{-1}$) and approximately $1.1$ km s$^{-1}$ Mpc$^{-1}$ when $\Sigma m_\nu$ is allowed to vary, demonstrating a competitive, independent test of the need for new recombination physics. The results underscore the role of priors, particularly on $A_s$ and $\Sigma m_\nu$, in shaping neutrino-mass–inference and $H_0$ outcomes within this framework.

Abstract

We present a sound-horizon-agnostic determination of the Hubble constant, $H_0$, by combining DESI DR2 baryon acoustic oscillation (BAO) data with the latest cosmic microwave background (CMB) lensing measurements from Planck, ACT, and SPT-3G, the angular size of the CMB acoustic scale, Dark Energy Survey Year-3 ($3\times2$-pt) galaxy weak lensing and clustering correlations, and the Pantheon+ supernova sample. In this analysis, The sound horizon at the drag epoch, $r_d$, is treated as a free parameter. By combining uncalibrated comoving distances from BAO and supernovae with constraints on the matter density $Ω_m h^2$ from CMB and galaxy lensing/clustering, we break the $r_d$-$H_0$ degeneracy and obtain $H_0 = 70.0 \pm 1.7$ km/s/Mpc when the sum of the neutrino masses is fixed at $Σm_ν= 0.06$ eV. With an informative prior on the amplitude of primordial fluctuations, $A_s$, we find $H_0 = 70.03 \pm 0.97$ km/s/Mpc. Allowing $Σm_ν$ to vary, we find that the neutrino mass is weakly constrained and strongly prior-dependent. Consequently, the inferred $H_0$ is sensitive to the choice of the $Σm_ν$ prior, with a uniform prior biasing results toward larger neutrino masses and higher $H_0$, while a logarithmic prior reduces this bias significantly. Forecasts for the completed DESI BAO program, combined with Simons-Observatory-like CMB lensing, next-generation $3\times2$-pt data, and expanded supernova samples predict $σ(H_0) \simeq 0.67$ km/s/Mpc with fixed $Σm_ν$, and $σ(H_0) \simeq 1.1$ km/s/Mpc with $Σm_ν< 0.133$ ($<0.263$) eV at 68% (95%) CL when $Σm_ν$ is varied.

Figures (5)

• Figure 1: Relative difference in the CMB lensing convergence spectrum $C_\ell^{\kappa \kappa}$ for a modified recombination model with an $r_d$ smaller by 2%, relative to the Planck best-fit $\Lambda$CDM model. Orange points, green stars, and red triangles with error bars show the $C_\ell^{\kappa \kappa}$ bandpowers from ACT, Planck, and SPT-3G, respectively. The figure illustrates that recombination changes capable of raising $H_0$ to $\sim 72$ km/s/Mpc have only a minor effect on the CMB lensing spectrum.
• Figure 2: Relative differences in the galaxy clustering correlation functions $w_{ij}(\theta)$ and $\gamma_{t,ij}(\theta)$, in four redshift bins ($i=j=1,\dots,4$), with respect to the prediction of the Planck+DES Y3 best-fit $\Lambda$CDM model. Blue points show the DES Y3 measurement residuals with uncertainties, and the solid yellow curve corresponds to the same modified-recombination model as in Fig. \ref{['fig:rec_indep']}. The figure demonstrates that the DES Y3 $3\times2$ pt observables are essentially insensitive to modifications of the recombination history.
• Figure 3: The 68% and 95% CL contours and the 1D marginalized posterior distributions for $H_0$, $\Omega_m h^2$, $\Omega_m$, and $\Sigma m_\nu$ from current data. The elongated 2D contours of $H_0$, $\Omega_m h^2$ and $\Sigma m_\nu$ highlight the positive correlations between these parameters discussed in the text. The DESI2+Planck+APS-L+DESY3+PP analysis uses the full Planck data, with $r_d$ as a derived parameter computed using the standard recombination routine in CAMB. In the analyses of all other data combinations in this figure, $r_d$ is a free parameter.
• Figure 4: The 68% and 95% CL contours, along with the 1D marginalized posterior distributions for $H_0$, $\Omega_m h^2$, and $\Sigma m_\nu$ from current data, comparing the results obtained with a uniform prior and a logarithmic prior on $\Sigma m_\nu$. This figure illustrates how using a logarithmic prior eliminates the apparent bias towards higher values of $H_0$ and $\Omega_mh^2$.
• Figure 5: The forecasted 68% and 95% CL posterior distributions for $H_0$, $\Omega_m h^2$, $\Omega_m$, and $\Sigma m_\nu$. For reference, the green dashed lines represent the fiducial values used in the forecast.