Expansion-history preferences of DESI DR2 and external data

We explore the origin of the preference of DESI DR2 baryon acoustic oscillation (BAO) measurements and external data from cosmic microwave background (CMB) and type Ia supernovae (SNIa) that dark energy behavior departs from that expected in the standard cosmological model with vacuum energy ($Λ$CDM). In our analysis, we allow a flexible scaling of the expansion rate with redshift that nevertheless allows reasonably tight constraints on the quantities of interest, and adopt and validate a simple yet accurate compression of the CMB data that allows us to constrain our phenomenological model of the expansion history. We find that data consistently show a preference for a 3-4 % increase in the expansion rate at $z\simeq 0.7$ relative to that predicted by the standard $Λ$CDM model, in excellent agreement with results from the less flexible $(w_0, w_a)$ parameterization which was used in previous analyses. Even though our model allows a departure from the best-fit $Λ$CDM model at zero redshift, we find no evidence for such a signal. We also find no evidence (at greater than 1$σ$ significance) for a departure of the expansion rate from the $Λ$CDM predictions at higher redshifts for any of the data combinations that we consider. Overall, our results strengthen the robustness of the findings using the combination of DESI, CMB, and SNIa data to dark-energy modeling assumptions.

💡 Research Summary

The paper investigates whether the apparent preference for dynamical dark energy seen in recent analyses of DESI DR2 baryon acoustic oscillation (BAO) data, when combined with external cosmic microwave background (CMB) and type‑Ia supernova (SNIa) observations, is driven by the specific parameterisation of the dark‑energy sector or reflects a genuine feature of the expansion history. To answer this, the authors adopt a phenomenological “modified‑H” model that directly perturbs the Hubble expansion rate in six redshift bins, rather than imposing a smooth equation‑of‑state w(a)=w₀+ wₐ(1−a). The model is defined as

H(z)=H_LCDM · E(z) · (1+α_i)

where H_LCDM is the standard ΛCDM Hubble constant, E(z) is the usual ΛCDM dimensionless expansion function, and α_i (i=1…6) are free parameters that scale the expansion rate in the six bins that roughly coincide with the DESI DR2 BAO bins (0<z<0.4, 0.4–0.6, 0.6–0.8, 0.8–1.1, 1.1–1.6, 1.6–4.0). The lowest bin is extended down to z=0 so that H(z=0) can vary independently of the fixed H_LCDM value, allowing the analysis to test any tension in the local Hubble constant. The physical baryon density Ω_b h² and cold‑dark‑matter density Ω_cdm h² are also varied, while the Hubble constant is fixed to its best‑fit ΛCDM value for the modified‑H runs.

Data sets used are:

1. DESI DR2 BAO: 13 compressed distance measurements and their covariance (Table IV of the DESI DR2 BAO paper). The authors deliberately avoid the full‑shape clustering information to keep the analysis as model‑independent as possible.
2. A compressed CMB likelihood: three summary parameters – the shift parameter R, the angular scale ℓ_a, and Ω_b h² – derived from the joint Planck PR3 and ACT DR6 likelihoods. The compression reproduces the full CMB constraints for ΛCDM and also for the (w₀,wₐ) model, as shown in Appendix A.
3. Three SNIa compilations: DES‑Year 5 (DESY5), Union3, and PantheonPlus. All three are treated with an analytic marginalisation over the absolute‑magnitude offset M.

The modified‑H model is implemented by adapting CAMB to compute distances and supernova magnitudes for any set of α_i, and the posterior is sampled with Cobaya’s MCMC engine, using the Gelman‑Rubin R < 0.01 convergence criterion. Parameter priors are flat and listed in Table I.

Key results:

• Across all data combinations, the α parameters are consistent with zero (the ΛCDM prediction) except for a modest ∼2 σ upward shift in the third bin (0.6 ≤ z < 0.8). This corresponds to a 3–4 % increase in the expansion rate at z≈0.7 relative to the ΛCDM best‑fit curve.
• The significance of this “bump” is 2.6 σ for DESI + CMB alone, and 2.4–2.7 σ when any of the three SNIa samples are added. The magnitude and redshift location of the bump match very well the feature previously reported in analyses that used the (w₀,wₐ) parameterisation.
• No statistically significant deviation is found at z≈0 (the Hubble constant) or at higher redshifts (z ≳ 1.5). The data are compatible with ΛCDM within 1 σ in those regimes.
• The overall χ² of the modified‑H model is slightly lower than that of the (w₀,wₐ) model, but the improvement is not enough to overcome the penalty for the additional parameters (i.e., no strong Bayesian evidence for the more complex model).
• The compressed CMB likelihood works well for this phenomenological approach, confirming that the three‑parameter compression captures the relevant geometric information for dark‑energy studies.
• The consistency of the bump across all three SNIa compilations demonstrates that the signal is not driven by a particular supernova data set.

Interpretation: The analysis shows that a flexible, piecewise‑constant perturbation of H(z) reproduces the same mild preference for a higher expansion rate at intermediate redshifts that was previously interpreted as evidence for dynamical dark energy in the (w₀,wₐ) framework. Because the modified‑H model does not enforce any continuity or physical equation‑of‑state across redshift, the result indicates that the data themselves contain a localized preference for a ∼3 % higher H(z) around z≈0.6–0.8. However, the statistical significance remains below the 3 σ threshold, and there is no corroborating evidence for deviations at lower or higher redshifts. Consequently, the authors conclude that the DESI + CMB + SNIa combination robustly points to a modest, localized feature in the expansion history, but the evidence is not strong enough to claim a detection of dynamical dark energy. Future surveys with higher precision BAO measurements, improved CMB polarization data, and larger, better‑calibrated supernova samples will be required to confirm or refute this hint.

In summary, the paper provides a model‑independent validation of earlier findings: DESI DR2 BAO data, when combined with compressed CMB and various SNIa samples, consistently suggest a 3‑4 % increase in the Hubble expansion rate at z≈0.7. The result is robust against the choice of dark‑energy parameterisation, but its statistical weight remains modest, underscoring the need for next‑generation cosmological observations to settle the question of whether dark energy truly evolves with time.