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

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.

💡 Research Summary

The paper tackles a subtle but important loophole in the widely‑cited “no‑go theorem” that rules out post‑recombination (late‑time) solutions to the Hubble tension. The theorem rests heavily on Baryon Acoustic Oscillation (BAO) measurements, which are extracted from galaxy‑clustering data using a pipeline that assumes a fiducial ΛCDM cosmology at several stages (distance‑redshift conversion, template construction, mock‑catalog covariance estimation, and reconstruction). The authors adopt a devil’s‑advocate stance: they assume that this fiducial‑ΛCDM choice systematically biases the low‑redshift acoustic angular scale (θ_d) low, i.e., the inferred product r_d H₀ is underestimated. They model this bias as a redshift‑independent rescaling that would shift the BAO‑derived H₀ upward toward the local SH0ES value.

To test whether such a bias could rescue a variety of late‑time dark‑energy (DE) models, they consider six representative extensions: wCDM, CPL (w₀–w_a) parametrisation, phenomenological emergent DE, holographic DE, the sign‑switching Λ_sCDM model, and a model with a negative cosmological constant. For each model they perform a Bayesian analysis combining three data sets: (i) “unanchored” Type Ia supernovae (SNe Ia) – i.e., supernova distance moduli without any absolute calibration, which constrain the shape of the expansion history up to z≈2; (ii) the BAO measurements after applying the assumed systematic shift; and (iii) geometric information from the Cosmic Microwave Background (CMB), primarily the angular‑diameter‑distance constraint that ties Ω_m to r_d H₀.

The key findings are:

1. Unanchored SNe Ia tightly fix the shape of E(z). Even without an absolute distance scale, the supernova Hubble diagram forces any viable model to follow a ΛCDM‑like expansion history for 0 ≲ z ≲ 2. This leaves little room for DE dynamics to raise H₀ while still fitting the supernova data.

2. Ω_m cannot be lowered arbitrarily. To compensate for the BAO bias and achieve a high H₀, one would need Ω_m ≈ 0.2 or less. However, the CMB angular‑diameter‑distance measurement strongly prefers Ω_m≈0.3, so such low values create a severe tension with the CMB geometry.

3. All tested DE models fail to resolve the tension. When Ω_m is kept within the CMB‑allowed range, the rescaled BAO data still imply r_d H₀ values far below the SH0ES result. Consequently, none of the six models can simultaneously satisfy the BAO, SNe Ia, and CMB constraints while delivering H₀≈73 km s⁻¹ Mpc⁻¹.

4. Λ_sCDM is the least disfavoured but not sufficient. The sign‑switching cosmological constant model offers a slightly broader viable parameter space because its late‑time dynamics can mimic a modest reduction in Ω_m, yet it still cannot bridge the full H₀ gap.

The authors conclude that even a generous, redshift‑independent BAO miscalibration cannot open a loophole in the no‑go theorem. BAO measurements remain powerful because they constrain both the standard‑ruler product r_d H₀ and the redshift evolution E(z). Moreover, the analysis highlights the underappreciated power of unanchored SNe Ia in ruling out late‑time modifications: the supernova shape information alone eliminates most DE‑driven attempts to raise H₀. Therefore, viable resolutions to the Hubble tension must invoke new physics operating before recombination (e.g., early dark energy, modified pre‑recombination expansion, or altered sound‑horizon physics) rather than relying on post‑recombination alterations.