Newest measurements of Hubble constant from DESI 2024 BAO observations

Technical Summary: Newest Measurements of Hubble Constant from DESI 2024 BAO Observations

Problem Statement
The paper addresses the persistent "Hubble tension," a significant discrepancy between measurements of the Hubble constant ($H_0$) derived from the early Universe (e.g., Planck CMB data yielding $H_0 \approx 67.4$ km s$^{-1}$ Mpc$^{-1}$) and those from the late Universe (e.g., SH0ES SN Ia data yielding $H_0 \approx 73.04$ km s$^{-1}$ Mpc$^{-1}$). This tension, currently at a significance level of 5–6$\sigma$, challenges the standard $\Lambda$CDM cosmological model. Previous attempts to resolve this using Baryon Acoustic Oscillations (BAO) often relied on the sound horizon scale ($r_d$) at the drag epoch as a standard ruler, effectively introducing a prior dependent on early-Universe physics or CMB calibration. The authors aim to determine $H_0$ using a purely data-driven, model-independent approach that circumvents the need for $r_d$ calibration or the intrinsic luminosity calibration of Type Ia Supernovae (SN Ia).

Methodology
The authors utilize the latest BAO measurements from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1), covering the redshift range $z = 0.51 - 2.33$. The core of their method relies on the Distance Duality Relation (DDR), $d_L(z) = (1+z)^2 d_A(z)$, which links luminosity distance ($d_L$) and angular diameter distance ($d_A$) in any metric theory of gravity where photon number is conserved.

The Hubble constant is formulated as:
$$H_0 = \frac{1}{(1+z)^2} \frac{\Xi_{\text{SNIa}}(z)}{\Xi_{\text{BAO}}(z)} H_{\text{CC}}(z)$$
where:

• $\Xi_{\text{SNIa}}(z) = H_0 d_L(z)$ is the unanchored luminosity distance derived from SN Ia apparent magnitudes.
• $\Xi_{\text{BAO}}(z) = H(z) d_A(z)$ is derived from DESI BAO measurements of transverse ($D_M$) and line-of-sight ($D_H$) comoving distances. Crucially, the ratio $D_M/D_H$ allows the calculation of $H(z)d_A(z)$ without knowing the absolute value of the sound horizon $r_d$.
• $H_{\text{CC}}(z)$ is the Hubble parameter measured directly via cosmic chronometers (CC).

To evaluate this equation at the specific redshifts of the five DESI BAO data points, the authors employ Gaussian Process (GP) regression to reconstruct the continuous functions of $H_0 d_L(z)$ (from the Pantheon+ SN Ia dataset) and $H(z)$ (from a compilation of 32 CC measurements). The GP regression uses the $\Lambda$CDM model as a prior mean function but is designed to be model-independent in its final output, selecting the best-fitting curves based on $\chi^2$ minimization. The analysis marginalizes over systematic uncertainties using covariance matrices for both SN Ia and CC data.

Key Contributions

1. Model-Independent $H_0$ Determination: The paper demonstrates a method to constrain $H_0$ using BAO data without relying on the sound horizon scale ($r_d$) or the absolute magnitude calibration of SN Ia ($M_B$). This eliminates the circularity often found in distance-ladder analyses that depend on early-Universe priors.
2. Integration of DESI DR1: The study incorporates the latest high-precision DESI BAO measurements, which offer a higher precision (approx. 0.49%) on the isotropic scale compared to previous SDSS surveys, despite covering only half the intended survey area.
3. Robust Reconstruction: By using GP regression with a fiducial $\Lambda$CDM prior, the authors show that the reconstruction results are robust against the choice of mean function (comparing $\Lambda$CDM and $w_0w_a$CDM) and the number of reconstructed curves, confirming the method's stability.

Results
Using the joint constraints from five DESI BAO redshifts ($z = 0.51, 0.706, 0.93, 1.317, 2.33$), the authors derive a Hubble constant of:
$$H_0 = 68.4^{+1.0}_{-0.8} \text{ km s}^{-1} \text{ Mpc}^{-1}$$
at a 68% confidence level, corresponding to an accuracy of 1.3%.

• Consistency: This result is in excellent agreement (within 1$\sigma$) with the Planck CMB results ($67.4 \pm 0.5$) and the Tip of the Red Giant Branch (TRGB) results ($68.5 \pm 1.5$).
• Tension: The measurement remains in a 4.3$\sigma$ tension with the SH0ES project results ($73.04 \pm 1.04$).
• Sensitivity Analysis: The authors note that the inclusion of the Luminous Red Galaxy (LRG) tracer introduces a non-negligible influence. Excluding specific LRG data points shifts the result slightly (e.g., to $69.7^{+1.1}_{-1.0}$ without LRG1), highlighting potential systematic effects in the LRG tracer that warrant future investigation in DESI 3-year and 5-year data.
• High-Redshift Extrapolation: The analysis acknowledges that the Lyman-$\alpha$ point ($z=2.33$) lies outside the redshift range of the SN Ia and CC data, potentially introducing bias. Excluding this point yields a corrected estimate of $68.6 \pm 1.0$ km s$^{-1}$ Mpc$^{-1}$, which remains consistent with the primary result.

Significance
The paper claims that this result provides a fundamental cosmological measurement with minimal assumptions, relying solely on data-driven reconstructions. The authors argue that the persistence of the tension between their DESI-based result and the SH0ES local measurements suggests that the Hubble tension is not merely a discrepancy between low-redshift and high-redshift observations (since DESI probes intermediate redshifts), but rather points to a deeper physical difference between the early and late Universe. The work supports the validity of the standard $\Lambda$CDM model's expansion history while highlighting the need to investigate systematic effects in local distance ladders or new physics in the early Universe to resolve the remaining tension.