The trouble with $H_0$ (1607.05617v2)

Abstract: We perform a comprehensive cosmological study of the $H_0$ tension between the direct local measurement and the model-dependent value inferred from the Cosmic Microwave Background. With the recent measurement of $H_0$ this tension has raised to more than $3\sigma$. We consider changes in the early time physics without modifying the late time cosmology. We also reconstruct the late time expansion history in a model independent way with minimal assumptions using distances measures from Baryon Acoustic Oscillations and Type Ia Supernovae, finding that at $z<0.6$ the recovered shape of the expansion history is less than 5 % different than that of a standard LCDM model. These probes also provide a model insensitive constraint on the low-redshift standard ruler, measuring directly the combination $r_s h$ where $H_0=h \times 100$ km/s/Mpc and $r_s$ is the sound horizon at radiation drag (the standard ruler), traditionally constrained by CMB observations. Thus $r_s$ and $H_0$ provide absolute scales for distance measurements (anchors) at opposite ends of the observable Universe. We calibrate the cosmic distance ladder and obtain a model-independent determination of the standard ruler for acoustic scale, $r_s$. The tension in $H_0$ reflects a mismatch between our determination of $r_s$ and its standard, CMB-inferred value. Without including high-l Planck CMB polarization data (i.e., only considering the "recommended baseline" low-l polarisation and temperature and the high l temperature data), a modification of the early-time physics to include a component of dark radiation with an effective number of species around 0.4 would reconcile the CMB-inferred constraints, and the local $H_0$ and standard ruler determinations. The inclusion of the "preliminary" high-l Planck CMB polarisation data disfavours this solution.

• The paper reveals that the H0 tension exceeds 3σ, highlighting significant discrepancies between local Cepheid-calibrated supernova data and CMB-derived measurements.
• It examines early-time physics modifications, such as extra dark radiation and variations in neutrino species, to assess their effects on H0 and sound horizon constraints.
• Model-independent distance ladder calibrations and spline reconstructions underscore limitations of the ΛCDM model, suggesting the need for new physics.

The Trouble with $H_0$: A Comprehensive Study of the Hubble Constant Tension

The paper entitled "The Trouble with $H_0$" presents an extensive analysis of the persistent tension between the Hubble constant ($H_0$) value deduced from local measurements and the value inferred from Cosmic Microwave Background (CMB) observations. This discrepancy has garnered significant attention because it challenges the assumptions underpinning the standard $\Lambda$CDM cosmological model, which provides a remarkably accurate description of the Universe. Given the implications for fundamental cosmological parameters and potential new physics, examining the causes and possible solutions to the $H_0$ tension is crucial.

Key Insights and Findings

• $H_0$ Discrepancy: The authors emphasize the discrepancy between direct local measurements of $H_0$—such as those from Cepheid-calibrated Type Ia Supernovae—and the model-dependent value derived from CMB data. The tension now exceeds $3\sigma$, indicating a potential systemic issue rather than statistical fluctuation.
• Early-Time Physics Modifications: Exploring deviations from standard early-time physics, the paper introduces extra relativistic energy components, often parameterized by an effective number of neutrino species, $N_{\rm eff}$. The analysis reveals that incorporating additional dark radiation could alleviate some of the tension, but only when specific datasets (such as high-$\ell$ polarization data) are selectively excluded.
• Primordial Helium and Sound Horizon: Constraints involving the primordial helium content ($Y_{\rm P}$) and the sound horizon at radiation drag ($r_{\rm s}$) are scrutinized. While altering these parameters could affect $H_0$ and $r_{\rm s}$ constraints, they do not reconcile the CMB and local measurements within observational limits.
• Late-Time Cosmology Adjustments: The paper examines changes to the late-time cosmic expansion history. Using model-independent methods such as cubic spline reconstruction of the Hubble parameter $H(z)$, the paper reveals that the expansion history is constrained to not deviate significantly from $\Lambda$CDM at redshifts below 0.6. This analysis underscores the robustness of the standard model's expansion history but suggests misalignment at the level of the absolute scale (i.e., $H_0$ and $r_{\rm s}$ anchor points).
• Model-Independent Distance Ladder Calibration: A key component of the research is the evaluation of $H_0$ and $r_{\rm s}$ without assuming the standard early-time physics. This approach finds a lower $r_{\rm s}$ than the Planck-inferred value, reinforcing the tension between local and high-redshift measurements and suggesting a need to reassess early Universe assumptions.

Implications and Future Directions

The findings highlight the potential necessity of revisiting standard cosmological assumptions, particularly those concerning the early Universe. If local $H_0$ measurements and CMB-derived values remain irreconcilable, the discrepancy could indicate new physics beyond the $\Lambda$CDM model, such as interaction models involving dark matter and radiation or evolving dark energy components.

This paper underscores the importance of cross-comparison among independent datasets and methodologies to resolve $H_0$ tension robustly. Further improvements in both observational precision and theoretical modeling are crucial. Future CMB observations, enhanced local $H_0$ determination efforts, and the utilization of complementary probes like gravitational wave standard sirens could provide new insights into this longstanding issue.

In conclusion, "The Trouble with $H_0$" presents a comprehensive analysis, suggesting that the tension between $H_0$ values from different measurement approaches remains a significant challenge for cosmology. This work paves the way for future investigations into new physics and methodology improvements in pursuit of a consistent cosmological model.