New physics in light of the $H_0$ tension: an alternative view
Sunny Vagnozzi
备注：
28 pages, 10 figures. Added references and discussion on physical models able to fix w or Neff to non-standard values (Section IVD). Clarified the aim of this work more clearly (I am not trying to evade or ignore additional degrees of freedom), many thanks to the referee for help! Abstract abridged. The busy reader should skip to Fig. 1, 2, 4, 5, and 10
The strong discrepancy between local and inverse distance ladder estimates of the Hubble constant $H_0$ could be pointing towards new physics beyond $Λ$CDM. Several attempts to address this tension through new physics rely on extended models, featuring extra free parameters beyond the 6 $Λ$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 $Λ$CDM. However, models that predict $N_{\rm eff} \approx 3.45$ would be able to bring the tension down to $1.5σ$ while only being weakly disfavored with respect to $Λ$CDM, whereas models that predict $w \approx -1.1$ would be able to bring the tension down to $2σ$ (at the cost of the preference for $Λ$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 $H_0$.
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