New physics in light of the $H_0$ tension: an alternative view (1907.07569v2)

Abstract: The strong discrepancy between local and inverse distance ladder estimates of the Hubble constant $H_0$ could be pointing towards new physics beyond $\Lambda$CDM. Several attempts to address this tension through new physics rely on extended models, featuring extra free parameters beyond the 6 $\Lambda$CDM parameters. However, marginalizing over extra parameters has the effect of broadening the uncertainties on the inferred parameters, and it is often the case that within these models the $H_0$ tension is addressed due to larger uncertainties rather than a genuine shift in the central value of $H_0$. What happens if a physical theory is able to fix the extra parameters to a specific set of non-standard values? The degrees of freedom of the model are reduced with respect to the standard case where the extra parameters are free to vary. Focusing on the dark energy equation of state $w$ and the effective number of relativistic species $N_{\rm eff}$, I find that physical theories able to fix $w \approx -1.3$ or $N_{\rm eff} \approx 3.95$ would lead to an estimate of $H_0$ from CMB, BAO, and SNeIa data in perfect agreement with the local distance ladder estimate, without broadening its uncertainty. These two non-standard models are, from a model-selection perspective, strongly disfavoured with respect to $\Lambda$CDM. However, models that predict $N_{\rm eff} \approx 3.45$ would be able to bring the tension down to $1.5\sigma$ while only being weakly disfavored with respect to $\Lambda$CDM, whereas models that predict $w \approx -1.1$ would be able to bring the tension down to $2\sigma$ (at the cost of the preference for $\Lambda$CDM being definite). Finally, I estimate dimensionless multipliers relating variations in $H_0$ to variations in $w$ and $N_{\rm eff}$, which can be used to repeat the analysis of this paper in light of future more precise local distance ladder estimates of $H_0$.

• The paper investigates fixing nonstandard values (w ≈ -1.3 and Nₑff ≈ 3.95) to shift the H₀ posterior without increasing parameter uncertainty.
• It employs fixed-parameter models (overline{w}CDM and overline{N}ΛCDM) to directly compare tension reduction and Bayesian evidence against extended ΛCDM scenarios.
• Findings show that although fixed values can lower the H₀ tension, they remain statistically disfavored compared to standard ΛCDM models.

Analyzing New Physics in Light of the $H_0$ Tension

In the article under discussion, Vagnozzi addresses the current tension between local and early-time estimates of the Hubble constant, $H_0$. This discrepancy exceeds the $3\sigma$ level and suggests potential new physics beyond the $\Lambda$CDM model. The paper questions whether solutions involving additional parameters in extended cosmological models genuinely resolve this tension, or simply increase parameter uncertainties. It explores an alternative approach: are there theoretical frameworks that can fix specific parameters like the dark energy equation of state $w$ or the effective number of relativistic species $N_{\rm eff}$ to particular non-standard values? Such a hypothesis would not only aim to resolve the $H_0$ tension without increasing uncertainties but also maintain the number of parameters as in $\Lambda$CDM, potentially yielding a better Bayesian evidence score.

The core objective is to identify values of $w$ and $N_{\rm eff}$ that align high-redshift estimates of $H_0$ (from CMB, BAO, and SNe data) with local measurements. Specifically, it was found that $w \approx -1.3$ or $N_{\rm eff} \approx 3.95$ achieve this alignment. These values seem extreme; indeed, models predicting them are strongly disfavored relative to $\Lambda$CDM with $\ln B_{ij} = -14.9$ and $-5.5$, respectively.

Vagnozzi's investigation is framed within two models: $\overline{w}$CDM, where $w$ is fixed but allowed to deviate into the phantom regime ($w < -1$), and $\overline{N}\Lambda$CDM, where $N_{\rm eff}$ is held constant at values greater than $3.046$. These models are pitted against traditional extensions where $w$ and/or $N_{\rm eff}$ are free to vary, increasing the complexity of the model by introducing additional parameters.

A salient feature of the paper is the comparison of tension levels and Bayesian evidence between non-standard models and their extended counterparts. The findings reveal that while conventional extensions reduce the $H_0$ tension to $1.4\sigma-1.9\sigma$, they do so by broadening the posterior distribution of $H_0$. Conversely, models improving agreement through fixed non-standard values achieve this by genuinely shifting the posterior distribution, not merely expanding it.

Furthermore, dimensionless multipliers relating changes in $H_0$ to changes in $w$ and $N_{\rm eff}$ were assessed, offering a quantitative analysis of how central $H_0$ values shift with varying parameters. These are valuable for iterative analysis with evolving local measurements of $H_0$. Moreover, despite the apparent statistical favor in model simplicity, the stipulated non-standard values remain statistically disfavored in a Bayesian sense.

A fascinating insight from the analysis is a potential sweet spot where $N_{\rm eff} \approx 3.45$ reduces the tension significantly while maintaining weak Bayesian disfavor relative to $\Lambda$CDM. This suggests that the non-standard approach may not merely act as a speculative alternative but rather a viable path with careful theoretical backing.

The paper further infers the implications for future cosmological parameter interpretations. Although no current theory entirely fulfills the criteria for fixing $w$ or $N_{\rm eff}$ to the required values without conflict, particular models (e.g., vector-like dark energy and thermalized sterile neutrinos) could closely approximate these values. Such insights spur ongoing theoretical exploration, which might eventually correlate with observable phenomena.

In conclusion, Vagnozzi's work challenges prevalent methodologies in addressing the $H_0$ tension. By analyzing whether fixing specific non-standard parameter values could offer efficient resolution paths, the research pivots the focus towards new physics frameworks. While existing models remain theoretical exercises, the results both critique and refine the tools available in cosmological model comparison, supporting the latter's evolving framework. Moving forward, even the statistical interplay and theoretical premises hinted at might underscore a significant pivot in cosmological theory development, where precision measurement imposes new pathways in theoretical physics.