The strong discrepancy between local distance ladder and Cosmic Microwave Background ( CMB ) estimates of the Hubble constant H _ { 0 } could be pointing towards new physics beyond the concordance \Lambda CDM model .
Several attempts to address this tension through new physics rely on extended cosmological models , featuring extra free parameters beyond the 6 \Lambda CDM parameters .
However , marginalizing over additional parameters has the effect of broadening the uncertainties on the inferred parameters , and it is often the case that within these models the tension is addressed due to larger uncertainties rather than a genuine shift in the central value of H _ { 0 } .
In this paper I consider an alternative viewpoint : what happens if one chooses to fix the extra parameters to non-standard values instead of varying them ?
Focusing on the dark energy equation of state w and the effective number of relativistic species N _ { eff } , I find that fixing w \approx - 1.3 or N _ { eff } \approx 3.95 leads to a high-redshift estimate of H _ { 0 } in perfect agreement with the local distance ladder estimate , without broadening the uncertainty on the former .
These two figures can have interesting implications for model-building activity .
While such non-standard models are strongly disfavoured with respect to the baseline \Lambda CDM model , Bayesian evidence considerations show that they nonetheless perform surprisingly better than the corresponding extended models where w and/or N _ { eff } are allowed to vary , when reducing the H _ { 0 } tension to the same level of statistical significance .
Finally , I estimate dimensionless multipliers relating variations in H _ { 0 } to variations in w and N _ { eff } , which can be used to swiftly repeat the analysis of this paper in light of future more precise local distance ladder estimate of H _ { 0 } , should the tension persist .