The $H_0$ World Cup. I. Summary of the baseline group stage results
The Hubble tension has reached a nominal significance above $7σ$, while new high-precision measurements of the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) sharpen the test of proposed solutions. Using a common framework, we compare fourteen representative alternatives to the standard $Λ$ Cold Dark Matter ($Λ$CDM) model in light of up-to-date CMB, BAO and supernovae data to gauge their ability to resolve the tension. The models span late-time modifications, modified recombination, and exotic pre-recombination expansion histories driven by additional radiation or a localized dark energy injection. We evaluate each proposal with complementary frequentist and Bayesian measures of the residual calibration tension and of the improvement in the joint fit. Both approaches identify the same broad hierarchy. Early dark energy and early modified gravity models perform best, shifting the $H_0$ inference without local measurement priors toward $70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and reducing the residual discrepancy with SH0ES to approximately $2.5-3.6σ$, depending on the model and statistic, while receiving strong support over $Λ$CDM in the combined fit. Varying the electron mass at recombination yields an intermediate improvement, whereas the enhanced-radiation and late-time scenarios do not improve over $Λ$CDM. This Letter summarizes the group stage of the competition; in a companion paper (Paper II) we present the results of an exhaustive set of analyses and assess their robustness to variations in modeling assumptions and datasets.
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Fuecoco · 2026-07-20 11:17:58 EST
Summary
This paper presents a comparative analysis of 14 alternative cosmological models to the standard $\Lambda$CDM framework, focusing on their ability to alleviate the $H_0$ tension. Using a common analysis pipeline, the authors evaluate these models with both frequentist and Bayesian methods, incorporating CMB, BAO, and supernova data. Early dark energy and early modified gravity models show the most significant improvement in reducing the tension, shifting $H_0$ toward $70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and achieving residual tensions of $2.5$–$3.6\sigma$. Other models, such as enhanced radiation or late-time scenarios, do not improve over $\Lambda$CDM.
Mathematical/empirical assessment
The paper provides clear statistical metrics, including $\Delta_{\rm DMAP}$, AIC, and $\ln{\rm BF}$, to assess model performance. The results are consistent across frequentist and Bayesian frameworks, with Group E models (early dark energy) performing best. The evaluation of the varying electron mass model shows intermediate improvements, while other models fail to meet selection thresholds. The paper also discusses the impact of dataset variations and modeling assumptions.
Strengths
The study is well-structured, with a clear methodology for comparing models under a unified framework. The use of both frequentist and Bayesian approaches strengthens the robustness of the findings. The paper also highlights the importance of considering multiple statistics and provides a comprehensive overview of the models' performance.
Concerns
The paper does not provide detailed derivations of the statistical measures used, such as $\Delta_{\rm DMAP}$ or $\Delta_{\rm shift}$, which limits the depth of understanding for readers unfamiliar with the specific techniques. Additionally, the paper focuses primarily on empirical performance without delving into the physical motivations or theoretical implications of the models.
Final decision
Weak accept