New physics in light of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> tension: An alternative view

Abstract

The strong discrepancy between local and early-time (inverse distance ladder) estimates of the Hubble constant ${H}_{0}$ could be pointing towards new physics beyond the concordance $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Several attempts to address this tension through new physics rely on extended cosmological models, featuring extra free parameters beyond the six $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ parameters. However, marginalizing over additional parameters has the effect of broadening the uncertainties on the inferred parameters (including ${H}_{0}$), 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 ${H}_{0}$. In this paper I consider an alternative viewpoint: what happens if a physical theory is able to fix the extra parameters to a specific set of nonstandard values? In this case, 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 ${N}_{\mathrm{eff}}$, I find that physical theories able to fix $w\ensuremath{\approx}\ensuremath{-}1.3$ or ${N}_{\mathrm{eff}}\ensuremath{\approx}3.95$ would lead to an estimate of ${H}_{0}$ from cosmic microwave background, baryon acoustic oscillation, and type Ia supernovae data in perfect agreement with the local distance ladder estimate, without broadening the uncertainty on the former. These two nonstandard models are, from a model-selection perspective, strongly disfavored with respect to the baseline $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. However, models that predict ${N}_{\mathrm{eff}}\ensuremath{\approx}3.45$ would be able to bring the tension down to $1.5\ensuremath{\sigma}$ while only being weakly disfavored with respect to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, whereas models that predict $w\ensuremath{\approx}\ensuremath{-}1.1$ would be able to bring the tension down to $2\ensuremath{\sigma}$ (at the cost of the preference for $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ being definite). Finally, I estimate dimensionless multipliers relating variations in ${H}_{0}$ to variations in $w$ and ${N}_{\mathrm{eff}}$, which can be used to swiftly repeat the analysis of this paper in light of future more precise local distance ladder estimates of ${H}_{0}$, should the tension persist. As a caveat, these results were obtained from the 2015 Planck data release, but these findings would be qualitatively largely unaffected were I to use more recent data.