$H_0$ Without the Sound Horizon (or Supernovae): A 2% Measurement in DESI DR1

Abstract

The sound horizon scale $r_s$ is a key source of information for early-time $H_0$ measurements, and is therefore a common target of new physics proposed to solve the Hubble tension. We present a sub-2% measurement of the Hubble constant that is independent of this scale, using data from the first data release of the Dark Energy Spectroscopic Instrument (DESI DR1). Building on previous work, we remove dependency on the sound horizon size using a heuristic rescaling procedure at the power spectrum level. A key innovation is the inclusion of \emph{uncalibrated} (agnostic to $r_s$) post-reconstruction BAO measurements from DESI DR1, as well as using the CMB acoustic scale $θ_*$ as a high-redshift anchor. Uncalibrated type-Ia supernovae are often included as an independent source of $Ω_m$ information; here we demonstrate the robustness of our results by additionally considering two supernova-independent alternative datasets. We find somewhat higher values of $H_0$ relative to our previous work: $69.2^{+1.3}_{-1.4}$, $70.3^{+1.4}_{-1.2}$, and $69.6^{+1.3}_{-1.8}\,{\rm km\,s^{-1}\,Mpc^{-1}}$ respectively when including measurements from i) Planck/ACT CMB lensing $\times$ unWISE galaxies, ii) the DES Year 3 6$\times$2pt analysis, and iii) Planck/ACT CMB lensing + the DES Year 5 supernova analysis. These remarkably consistent constraints achieve better than 2% precision; they are among the most stringent sound horizon-independent measurements from LSS to date, and provide a powerful avenue for probing the origin of the Hubble tension.

Figures (5)

• Figure 1: Top: The monopole ($\ell=0$; solid lines) and quadrupole ($\ell=2$; dashed lines) of the theoretical non-linear galaxy power spectrum are plotted for luminous red galaxies (LRGs) in the redshift range $0.4 < z < 0.6$. The wiggle-rescaling procedure detailed in Section \ref{['sec:theory_prev']} is illustrated for several values of $q_{\mathrm{BAO}}$; $q_{\mathrm{BAO}}=0.95$ is plotted in blue, $q_{\mathrm{BAO}}=1.0$ in orange, and $q_{\mathrm{BAO}}=1.05$ in green. $q_{\mathrm{BAO}}=1$ corresponds to $\Lambda$CDM, while larger values shift the BAO wiggles forward, and smaller values shift them backward, corresponding to a smaller/larger implied sound horizon scale respectively. Bottom: Residuals are shown versus the case $q_{\mathrm{BAO}} = 1$ for both multipoles $\ell = 0, 2$.
• Figure 2: Constraints on the parameters $H_0$, $\Omega_\mathrm{m}$, $\omega_\mathrm{b}$, and $q_{\mathrm{BAO}}$ using the DESI DR1 BAO measurements and a BBN prior on $\omega_\mathrm{b}$. In green: contours obtained when fixing $q_{\mathrm{BAO}} = 1$. As expected, these constraints closely match those obtained in the main DESI DR1 BAO analysis DESI2024.VI.KP7A. In orange: contours obtained when allowing the parameter $q_{\mathrm{BAO}}$ to vary. In the latter case, $H_0$ is no longer constrained, but importantly the $\Omega_\mathrm{m}$ constraints obtained in both cases are nearly identical.
• Figure 3: Contours are shown for the parameters $H_0$, $\Omega_\mathrm{m}$, $\ln{\left(10^{10} A_\mathrm{s}\right)}$, $n_{\mathrm{s}}$, and $q_{\mathrm{BAO}}$. In gray: constraints from the DESI DR1 full-shape galaxy clustering and the Ly$\alpha$ AP effect. This dataset also formed the base of our previous analysis Zaborowski:2025 and serves as a point of comparison. In red: same as gray, but additionally including DESI DR1 uncalibrated post-reconstruction BAO measurements. In blue: same as red, but also including a measurement of the CMB acoustic scale $\theta_*$ from Planck 2018 Planck:2020. All results shown include a BBN prior.
• Figure 4: Contours are shown for the parameters $H_0$, $\Omega_\mathrm{m}$, $\ln{\left(10^{10} A_\mathrm{s}\right)}$, $n_{\mathrm{s}}$, and $q_{\mathrm{BAO}}$. In blue: constraints are shown for the full DESI DR1 dataset (full-shape galaxy clustering + uncalibrated post-reconstruction BAO + the Ly$\alpha$ AP effect), plus the uncalibrated CMB acoustic scale $\theta_*$ measured in Planck 2018 Planck:2020. We note that this is the same as the blue contour in the previous Fig. \ref{['fig:desi_fs_bao_thetastar']}. In purple: same as blue, but additionally including Planck/ACT CMB lensing and the DES Y5 SN dataset. This dataset combination (excepting uncalibrated BAO and $\theta_*$) was also used in our previous work Zaborowski:2025 and serves as a point of comparison. In green: same as blue, but also including the Planck/ACT$\times$unWISE 3$\times$2pt dataset (Section \ref{['sec:data_actplanck']}). In orange: same as blue, but also including the DES Y3 6$\times$2pt dataset (Section \ref{['sec:data_des6x2pt']}). All results shown include a BBN prior.
• Figure 5: A whisker plot is shown of 68% confidence interval constraints for several representative measurements of the Hubble constant. From top to bottom: In black: $k_{\mathrm{eq}}$-based constraints from this work and our previous analysis Zaborowski:2025. In pink: constraints are shown from the main DESI DR1 full-shape + BAO analysis DESI2024.V.KP5. In blue: constraints from the main DESI DR1 BAO-only analysis DESI2024.VI.KP7A. In orange: $H_0$ constraints from the combined Planck/ACT CMB dataset. In green: late-time $H_0$ constraints from: i) the Chicago-Carnegie Hubble Program (CCHP; Freedman:2024), who used data from the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST), ii) the SH0ES team Riess:2022, who used data from HST, as well as iii) combined constraints from the largest combination of both subsamples available in JWST Riess:2024. JAGB stands for the J-region Asymptotic Giant Branch calibration method, and TRGB stands for calibration using the Tip of the Red Giant Branch (see references for additional details).