Late-time phenomenology required to solve the $H_0$ tension in view of the cosmic ladders and the anisotropic and angular BAO data sets

TL;DR

This study interrogates the H0 tension by enforcing standard prerecombination physics while letting late-time background evolution and SNIa calibration evolve. It employs a flexible, model-independent H(z) fit together with Gaussian Process–based reconstructions of M(z), constrained by SH0ES, Planck priors, BAO (3D and 2D), CCH, and Pantheon+ data. The results show that anisotropic (3D) BAO data favor a phantom-like rise in H(z) and a corresponding M(z) transition at very low redshift (z ≲ 0.2), whereas angular (2D) BAO data push the required changes to higher redshift (z ∼ 0.5–0.8) with possible negative DE density at z ≳ 2; both scenarios imply a violation of the weak energy condition and a crossing of the phantom divide, though the evidence is not definitive. The work underscores the critical impact of BAO data choice on proposed solutions to the H0 tension and highlights the need for model-independent BAO measurements and future data (e.g., Euclid) to robustly determine viable late-time histories.

Abstract

The $\sim 5σ$ mismatch between the value of the Hubble parameter measured by SH0ES and the one inferred from the inverse distance ladder (IDL) constitutes the biggest tension afflicting the standard model of cosmology, which could be pointing to the need of physics beyond $Λ$CDM. In this paper we study the background history required to solve the $H_0$ tension if we consider standard prerecombination physics, paying special attention to the role played by the data on baryon acoustic oscillations (BAO) employed to build the IDL. We show that the anisotropic BAO data favor an ultra-late-time (phantom-like) enhancement of $H(z)$ at $z\lesssim 0.2$, accompanied by a transition in the absolute magnitude of supernovae of Type Ia $M(z)$ in the same redshift range. This agrees with previous findings in the literature. The effective dark energy (DE) density must be smaller than in the standard model at higher redshifts. Instead, when angular BAO data (claimed to be less subject to model dependencies) is employed in the analysis, we find that the increase of $H(z)$ starts at much higher redshifts, typically in the range $z\sim 0.5-0.8$. In this case, $M(z)$ could experience also a transition (although much smoother) and the effective DE density becomes negative at $z\gtrsim 2$. Both scenarios require a violation of the weak energy condition (WEC), but leave an imprint on completely different redshift ranges and might also have a different impact on the perturbed observables. They allow for the effective crossing of the phantom divide. Finally, we employ two alternative methods to show that current data from cosmic chronometers do not exclude the violation of the WEC, but do not add any strong evidence in its favor neither. Our work puts the accent on the utmost importance of the choice of the BAO data set in the study of the possible solutions to the $H_0$ tension.

Figures (15)

• Figure 1: Degeneracy band at $68\%$ and 95$\%$ C.L. in the $M$-$r_d$ plane (in grey) inferred from uncalibrated BAO and SNIa data. We have obtained these constraints using the method previously employed in Gomez-Valent:2021hda, which is based on the Index of Inconsistency by Lin and Ishak Lin:2017ikq, see Appendix \ref{['sec:appendixA']} for details. We also include the vertical band with the SH0ES measurement of $M$ ($M^{R22}$) Riess:2021jrx and the horizontal band with the $\Lambda$CDM value of $r_d$ obtained by Planck ($r_d^{P18}$) Planck:2018vyg, both at 1$\sigma$ C.L. It is evident that the intersection of these two bands lie far away from the region preferred by the uncalibrated 3D BAO and SNIa data.
• Figure 2: Calibrated 3D and 2D BAO data, in red and blue, respectively. The calibration is carried out with the Planck/$\Lambda$CDM value of the sound horizon $r_d^{P18}$, see Sec. \ref{['sec:data']}. We also plot (in black) the curves of the various observables computed with the best-fit Planck/$\Lambda$CDM cosmology. See the comments in the first paragraph of Sec. \ref{['sec:results']}.
• Figure 4: Posterior distributions of the transition redshift $z_t$ obtained with the Baseline_3D and Baseline_2D data sets from the corresponding Monte Carlo analyses.
• Figure 5: Same as in Fig. \ref{['fig:H_M_3D_joined']}, but only for the curves with $0.09<z_t<0.15$. The vertical red band indicates the range of values of $z_t$ covered. In the middle plot, we include the constant values $M^{R22}$ (in cyan) and $M=-19.40$ (in purple), the latter being close to the $\Lambda$CDM best-fit value obtained from a CMB+BAO+SNIa analysis (see e.g. Gomez-Valent:2022hkb). In the bottom plot, we present the corresponding shapes of the deceleration parameter $q(z)$, Eq. \ref{['eq:q']}, and include an inner plot with the positive correlation between its value at $z=0$, $q_0$, and $z_t$.
• Figure 6: Curves of $\Delta(z)$ (Eq. \ref{['eq:Delta']}) obtained in the analysis of the baseline_3D data set with $z_{\rm max}=0.5$ (upper plot) and $z_{\rm max}=1$ (lower plot). They have been selected from the group of 68% curves with lowest $\chi^2$ in the Monte Carlo Markov chain and represent the typical behavior of $\Delta(z)$ required to solve the Hubble tension. The transition happens in both analyses at $z_t\lesssim 0.2$. See the main text for details.