On the Difficulties with Late-Time Solutions for the Hubble Tension

TL;DR

The paper assesses whether late-time modifications to the expansion history can resolve the Hubble tension between SH0ES and high-redshift probes by testing simple phenomenological models (Hstep, Mstep, Hstep+Mstep, and $w_0w_a$+Mstep) alongside a physically motivated non-minimally coupled scalar-field scenario, using DESI DR2 BAO, compressed CMB, and PantheonPlus+SH0ES data. It finds that late-time $H(z)$ changes alone struggle to fit all datasets; a sharp, very low-redshift ($z_t\approx0.01$) step in the SNIa absolute magnitude $M$ yields the largest gain (\Delta\chi^2\simeq-40) by effectively decoupling SH0ES, while more gradual or intermediate transitions provide only modest improvements. A scalar-field model with a gradual $M$-transition around $z_t\sim0.15$ can achieve $\Delta\chi^2\simeq-27$, illustrating partial reconciliation through modified gravity–driven magnitude evolution, but not a full solution. Including SBF measurements offers an independent cross-check, but current uncertainties keep the main conclusions intact, suggesting that dramatic late-time solutions without data decoupling are unlikely. Overall, the work reinforces the view that resolving the Hubble tension likely requires either decoupling SH0ES from higher-redshift data via magnitude evolution or invoking nonstandard distance-duality relations, rather than smooth late-time dynamics.

Abstract

We explore the notion that cosmological models that modify the late-time expansion history cannot simultaneously fit the SH0ES collaboration's measurements of the Hubble constant, DESI baryon acoustic oscillations data, and Type Ia supernova distances. Adopting a few simple phenomenological models, we quantitatively demonstrate that a satisfactory fit with a model with late-time expansion history can only be achieved if one of the following is true: 1) there is a sharp step in the absolute magnitude of Type Ia supernovae at very low redshift, $z\sim 0.01$, or 2) the distance duality relation, $d_L(z)=(1+z)^2d_A(z)$, is broken. Both solutions are trivial in that they effectively decouple the calibrated SNIa measurements from other data, and this qualitatively agrees with previous work built on studying specific dark-energy models. We also identify a less effective class of late-time solutions with a transition at $z\simeq 0.15$ that lead to a more modest improvement in fit to the data than models with a very low-z transition. Our conclusions are largely unchanged when we include surface brightness fluctuation distance measurements, with their current systematic uncertainties, to our analysis. We finally illustrate our findings by studying a physical model which, when equipped with the ability to smoothly change the absolute magnitude of Type Ia supernovae, partially resolves the Hubble tension.

Figures (6)

• Figure 1: Illustration of the inability of low-redshift dark-energy models to simultaneously fit the SH0ES measurements and other cosmological data. In both panels, we show the distance modulus relative to one predicted in the best-fit $\Lambda$CDM model as a function of redshift, along with the Cepheid measurements by SH0ES collaboration, SNIa data from DESY5, and BAO data from DESI DR2. The top panel shows the scenario in which SNIa are anchored to the SH0ES measurement; then a smooth model is unable to simultaneously fit the SNIa and BAO data in the region where they overlap. The lower panel shows the scenario where the SNIa data are instead anchored to BAO distances (as actually preferred by a global cosmological fit); then the Cepheid measurement is inconsistent with the rest of the Hubble diagram in which it effectively introduces a sharp break. See text for more details.
• Figure 2: Similar as Fig. \ref{['fig:tension']}, but for three phenomenological models, each compared to $\Lambda$CDM. From top to bottom these are a model with a sharp step in the expansion rate (Hstep), one with a step in the absolute magnitude of SNIa (Mstep), and one with the $w_0w_a$CDM expansion history and an Mstep. In each case, we provide in the legend the best-fit chi squared relative to $\Lambda$CDM ($\Delta\chi^2$), as well as the best-fit redshift of the step ($z_{\rm t}$). We also show data for the Cepheid calibrators, SNIa, and DESI BAO.
• Figure 3: Improvement of the goodness of fit, $\Delta\chi^2$, relative to the best-fit $\Lambda$CDM cosmological model, shown as a function of the transition redshift $z_{\rm t}$. We show results for the Mstep model, Hstep+Mstep (assuming the same transition redshift in the Hubble parameter and absolute magnitude), and the Mstep model embedded in ($w_0, w_a$) expansion history. In all three models, the largest improvement in the fit occurs with transition redshift of about 0.01. See text and Table \ref{['tab:results']} for more details.
• Figure 4: Similar as Figs. \ref{['fig:tension']} and \ref{['fig:Hstep']}, but for the physical scalar-field model discussed in Sec. \ref{['sec:Wolf_model']}. The fit of the model is acceptable ($\Delta\chi^2\simeq -27$ relative to $\Lambda$CDM) due to its ability to change the absolute magnitude of SNIa. While not as good a fit to the data as models with a very low-redshift ($z_{\rm t}\simeq 0.01$) transition, the model's reasonable fit is due in part to the fact that the transition at $z_{\rm t}\sim 0.15$ is gradual, as it fits the data in the intermediate redshift range better than models with a sharp transition. See text for more details.
• Figure 5: Tests of the replacement of the SH0ES dataset with an equivalent $M$-prior. We show constraints on the Hubble constant, matter density relative to critical, and absolute maggnitude of SNIa in the $\Lambda$CDM model. The solid grey contours show the fiducial case, the red contours show the case when the $M$ information is effectively double-counted, while the green contours show the corrected $M$ prior that approximately matches the fiducial constraints. See text for details.