BAO miscalibration cannot rescue late-time solutions to the Hubble tension

TL;DR

The paper investigates whether a fiducial-ΛCDM bias in BAO analyses could invalidate the no-go theorem against post-recombination solutions to the Hubble tension. By applying a redshift-independent rescaling of BAO data (λ ≈ 1.06) and testing seven late-time DE models against combinations of BAO, unanchored SNeIa, and compressed CMB data, the authors show that such a bias cannot reconcile a higher $H_0$ with CMB geometry once the full dataset is considered. Unanchored SNeIa play a crucial role in constraining the late-time expansion history, effectively ruling out most late-time loopholes even with BAO miscalibration; the Λ_sCDM model remains the most promising among those tested but falls short of fully solving the tension. The results strengthen the case for pre-recombination new physics as the essential ingredient to address the Hubble tension and highlight the robustness of the no-go theorem under fiducial-BAO systematics, while pointing to future work with full CMB likelihoods and expanded BAO/SNeIa datasets.

Abstract

Baryon Acoustic Oscillation (BAO) measurements play a key role in ruling out post-recombination solutions to the Hubble tension. However, because the data compression leading to these measurements assumes a fiducial $Λ$CDM cosmology, their reliability in testing late-time modifications to $Λ$CDM has at times been called into question. We play devil's advocate and posit that fiducial cosmology assumptions do indeed affect BAO measurements in such a way that low-redshift acoustic angular scales (proportional to the Hubble constant $H_0$) are biased low, and test whether such a rescaling can rescue post-recombination solutions. The answer is no. Firstly, strong constraints on the shape of the $z \lesssim 2$ expansion history from unanchored Type Ia Supernovae (SNeIa) prevent large deviations from $Λ$CDM. In addition, unless $Ω_m$ is significantly lower than $0.3$, the rescaled BAO measurements would be in strong tension with geometrical information from the Cosmic Microwave Background. We demonstrate this explicitly on several dark energy (DE) models ($w$CDM, CPL DE, phenomenologically emergent DE, holographic DE, $Λ_s$CDM, and the negative cosmological constant model), finding that none can address the Hubble tension once unanchored SNeIa are included. We argue that the $Λ_s$CDM sign-switching cosmological constant model possesses interesting features which make it the least unpromising one among those tested. Our results demonstrate that possible fiducial cosmology-induced BAO biases cannot be invoked as loopholes to the Hubble tension "no-go theorem", and highlight the extremely important but so far underappreciated role of unanchored SNeIa in ruling out post-recombination solutions.

Figures (15)

• Figure 1: Cartoon representation of a biased transverse BAO measurement at the effective redshift $z_{\text{eff}}$. We shall play devil's advocate (in grey) and assume that adopting a fiducial $\Lambda$CDM cosmology in the BAO pipeline biases the resulting angular scales low. This means that the true angular scale is larger than the inferred one, $\theta_d^{\cal R}>\theta_d$, and similarly for the Hubble constant, i.e. $H_0^{\cal R}>H_0$, whereas the converse holds for comoving angular diameter distances, i.e. $D_M^{\cal R}<D_M$. The superscript $^{\cal R}$ refers to "bias-corrected" BAO measurements.
• Figure 2: Best-fit reconstructed expansion histories for the seven late-time cosmological models studied in this work. The first seven panels (from left to right, up to down) show the predictions for $H(z)/(1+z)$ within each individual model, with best-fit parameters determined from five different dataset combinations, discussed later in Sec. \ref{['sec:datasets']}, and as determined by the color coding. This comparison illustrates the effect of using standard BAO (BAO) versus rescaled BAO (BAOr) measurements, and the powerful constraints imposed by including unanchored SNeIa (PP). A key feature across almost all models is that while the rescaled BAO data (base+BAOr dataset combination) can lead to significant shifts in the predicted expansion history, the inclusion of unanchored SNeIa data (base+BAOr+PP) largely precludes these shifts by tightly constraining the shape of the expansion history, pulling back the expansion history back towards the $\Lambda$CDM one. Finally, the bottom right panel directly compares the best-fit expansion histories for all seven models, as determined by the color coding, in light of the standard base+BAO+PP dataset combination.
• Figure 3: Triangular plot showing 2D joint and 1D marginalized posterior probability distributions for the fractional matter density parameter $\Omega_m$, the physical baryon density $\omega_b$, and the reduced Hubble constant $h \equiv H_0/(100\,{\text{km}}/{\text{s}}/{\text{Mpc}})$, obtained within the baseline $\Lambda$CDM model by combining a BBN prior on $\omega_b$ with standard (blue curves) or rescaled (red curves) BAO measurements. We clearly see that the effect of rescaling the BAO measurements transfers entirely to a rescaling of $H_0$, which controls the overall BAO calibration, whereas the inferred value of $\Omega_m$ is unchanged, since this parameter controls the (loosely constrained) shape of BAO measurements.
• Figure 4: Triangular plot showing 2D joint and 1D marginalized posterior probability distributions for the fractional matter density $\Omega_m$, the physical baryon density $\omega_b$, and the reduced Hubble constant $h \equiv H_0/(100\,{\text{km}}/{\text{s}}/{\text{Mpc}})$, obtained within the baseline $\Lambda$CDM model (see Sec. \ref{['subsec:lcdm']}) in light of the base+BAO (blue contours), base+BAOr (magenta contours), base+BAO+PP (red contours), base+PP (green contours), and base+BAOr+PP (black contours) dataset combinations. We recall that the base combination includes the P18$^{\star}$$2 \times 2$ compressed CMB likelihood as well as the $\Omega_m^{P}$ prior on $\Omega_m$.
• Figure 5: Upper panel: recombination sound horizon $\theta_s$ observed, inferred, or predicted at different redshifts. The black diamonds correspond to $\theta_s$ inferred from a selection of BAO measurements (the difference between sound horizon at recombination and at baryon drag has been taken into account when deducing these measurements), whereas the grey circles are the same values but after rescaling the BAO measurements. The red square at $z=z_{\star}$ corresponds to the CMB acoustic scale measurement. All datapoints come with uncertainties, but these are too small to be appreciated by the eye. The three curves correspond to the predictions for $\theta_s(z)$ within the three cosmological models discussed in the text: the best-fit cosmologies inferred from the base+BAO (blue curve) and base+BAOr (magenta curve) dataset combinations, and the "rigid shift" cosmology which is identical to best-fit base+BAO one, except for a shift in $H_0=73.0\,{\text{km}}/{\text{s}}/{\text{Mpc}}$ (yellow curve). Lower panel: normalized residuals. What is plotted are the differences between datapoints and model prediction for each of the three cosmologies shown in the upper panel, with the differences normalized by the uncertainty of the associated datapoint. For the diamond [circle] residuals the datapoints are the standard [rescaled] BAO measurements, and the model is the best-fit cosmology inferred from the base+BAO [base+BAOr] dataset combination; for the cross residuals the datapoints are the rescaled BAO measurements, whereas the model is the "rigid shift" cosmology.