The Hubble Hunter's Guide

TL;DR

The paper assesses the H0 tension between distance-ladder and CMB-inferred values within ΛCDM, surveying a broad spectrum of pre- and post-recombination modifications. It argues that viable resolutions likely require changes before recombination that increase the expansion rate, but such models face stringent constraints from the CMB damping tail and the radiation-driving envelope. Post-recombination solutions tend to struggle with BAO and Planck consistency unless introducing many new degrees of freedom, which can be penalized by model priors. The work emphasizes the need for improved high-ℓ, polarization, and lensing data to validate or falsify these proposed avenues and to illuminate the path toward resolving the H0 discrepancy.

Abstract

Measurements of the Hubble constant, and more generally measurements of the expansion rate and distances over the interval $0 < z < 1$, appear to be inconsistent with the predictions of the standard cosmological model ($Λ$CDM) given observations of cosmic microwave background temperature and polarization anisotropies. Here we consider a variety of types of departures from $Λ$CDM that could, in principle, restore concordance among these datasets, and we explain why we find almost all of them unlikely to be successful. We single out the set of solutions that increase the expansion rate in the decade of scale factor expansion just prior to recombination as the least unlikely. These solutions are themselves tightly constrained by their impact on photon diffusion and on the gravitational driving of acoustic oscillations of the modes that begin oscillating during this epoch -- modes that project on to angular scales that are very well measured. We point out that a general feature of such solutions is a residual to fits to $Λ$CDM, like the one observed in Planck power spectra. This residual drives the modestly significant inferences of angular-scale dependence to the matter density and anomalously high lensing power, puzzling aspects of a data set that is otherwise extremely well fit by $Λ$CDM.

Figures (2)

• Figure 1: $\Lambda$CDM tensions in the $r_{\rm s}^{\rm drag}-H_0$ plane. The orange and green shaded regions are 68% and 95% confidence regions from SH$_0$ES and from BOSS galaxy BAO + Pantheon, respectively. These inferences are largely independent of assumed cosmological model, as explained in the text. Conversely, the Planck contours assume $\Lambda$CDM is the correct model at all redshifts. We show three versions of the Planck constraints: those from the full Planck TT,TE,EE+lowE likelihood, and those from Planck TT+lowE with TT limited to either $\ell\,{<}\,800$ or $\ell\,{>}\,800$. The color coding indicates values of the matter density, $\omega_{\rm m}$. We see a strong correlation between $\omega_{\rm m}$, $H_0$, and $r_{\rm s}^{\rm drag}$. The direction swept out in the $r_{\rm s}^{\rm drag}-H_0$ plane by variations in $\omega_{\rm m}$ is not a direction that can reconcile all three datasets.
• Figure 2: On the left axis (the filled curves), we show the fractional linear response of the "visibility-averaged" $\bar{r}_{\rm s}$ and $\bar{r}_{\rm d}$ to a fractional change in $H(z)$ in some logarithmic interval in $z$ (see Appendix \ref{['app:visrsrd']} for exact definitions). For each curve, the dot-dashed line shows what the response would be without accounting for the dependence of the visibility function on $H(z)$. The right axes (dashed curves) show the fractional change in $H(z)$ relative to our $\Lambda$CDM fiducial model for two cases which reduce $\bar{r}_{\rm s}$. The first has $N_{\rm eff}\,{=}\,4.2$ (which lowers $\bar{r}_{\rm s}$ by 7%) and the second is the best-fit $\phi^4$ model from agrawal2019. One can read off the (linearized) change to $\bar{r}_{\rm s}$ and $\bar{r}_{\rm d}$ from these two models by multiplying the dashed lines by either the blue or orange regions, respectively, then integrating across $z$.