Expansion-history preferences of DESI DR2 and external data

Technical Summary: Expansion-history preferences of DESI DR2 and external data

Problem Statement
Recent analyses combining Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) baryon acoustic oscillation (BAO) measurements with Cosmic Microwave Background (CMB) and Type Ia supernovae (SNIa) data have indicated a statistical preference for dynamical dark energy, deviating from the standard $\Lambda$CDM model (where $w = -1$). Specifically, the popular $(w_0, w_a)$ parameterization suggests a "phantom" regime ($w < -1$) at high redshifts transitioning to $w > -1$ at low redshifts. However, the rigid nature of smooth parameterizations like $(w_0, w_a)$ may artificially enforce coherence across redshifts, making it difficult to determine if the data genuinely supports specific features (e.g., a deviation at low $z$ vs. high $z$) or if the preference is an artifact of the model's stiffness. The authors aim to identify precisely which features in the data drive the preference for dynamical dark energy without being constrained by smooth equation-of-state descriptions.

Methodology
The authors introduce a "modified-H" model that parameterizes the expansion rate $H(z)$ directly using piecewise-constant scaling factors, rather than modeling the dark energy equation of state $w(z)$.

• Model Definition: The Hubble parameter is defined as $H(z) = H_0^{\Lambda\text{CDM}} E(z) (1 + \alpha_i)$, where $E(z)$ is the standard $\Lambda$CDM expansion function, and $\alpha_i$ are free parameters representing deviations in six specific redshift bins.
• Redshift Binning: The bins are designed to align with the DESI DR2 BAO compression bins ($0.0 \le z < 0.4$, $0.4 \le z < 0.6$, $0.6 \le z < 0.8$, $0.8 \le z < 1.1$, $1.1 \le z < 1.6$, and $1.6 \le z < 4.16$). Crucially, the lowest bin extends to $z=0$, allowing $H(z=0)$ to vary independently of the high-redshift anchored $H_0^{\Lambda\text{CDM}}$.
• Data Sets: The analysis utilizes:
  • DESI DR2 BAO: 13 distance measurements and their covariance.
  • Compressed CMB: A validated compression of Planck (PR3) and Atacama Cosmology Telescope (ACT DR6) data into three physical quantities: the shift parameter $R$, the angular scale $\ell_a$, and the physical baryon density $\Omega_b h^2$.
  • SNIa: Primarily the Dark Energy Survey Year 5 (DESY5) dataset, with cross-checks using the Union3 and PantheonPlus compilations.
• Analysis: Constraints are derived using Monte Carlo Markov Chain (MCMC) sampling via the Cobaya framework, marginalizing over physical baryon and CDM densities.

Key Contributions

1. Flexible Expansion History: The paper demonstrates that a binned, piecewise-constant parameterization of $H(z)$ allows for rapid changes in the expansion rate that smooth $w(z)$ models cannot easily capture, while avoiding the large parameter-space degeneracies typical of binned equation-of-state models.
2. CMB Compression Validation: The authors provide and validate a simple, accurate compression of CMB data (Planck+ACT) into three parameters ($R, \ell_a, \Omega_b h^2$) that remains robust for phenomenological models where a full theoretical CMB power spectrum cannot be computed.
3. Decoupling Low-Redshift Behavior: By allowing $H(z=0)$ to vary independently, the model tests whether the data requires a departure from $\Lambda$CDM specifically at $z=0$ (relevant for the Hubble tension) versus at intermediate redshifts.

Results

• Preference for Expansion Rate Increase: The data consistently show a preference for a 3–4% increase in the expansion rate relative to the best-fit $\Lambda$CDM prediction at redshift $z \simeq 0.7$. This feature appears in all data combinations (DESI+CMB, and with DESY5, Union3, or PantheonPlus SNIa).
• Agreement with $(w_0, w_a)$: The results from the flexible modified-H model are in excellent agreement with the less flexible $(w_0, w_a)$ parameterization. Both models identify the same "bump" in $H(z)$ at $z \simeq 0.5\text{--}0.7$.
• Statistical Significance: The preference for the expansion rate bump is modest, ranging from 2.4$\sigma$ to 2.7$\sigma$ depending on the SNIa dataset used. It is not a high-significance detection.
• No Evidence for Low-$z$ or High-$z$ Deviations:
  • Despite the model allowing $H(z=0)$ to differ from the high-redshift anchored value, the data show no evidence for a departure from $\Lambda$CDM at $z \to 0$.
  • There is no evidence (at $>1\sigma$ significance) for deviations at higher redshifts ($z \gtrsim 1.5$) in any data combination.
• Model Fit: The modified-H model provides a slightly better fit to the data than the $(w_0, w_a)$ model, but the improvement is not sufficient to claim a preference for the more complex model.

Significance and Claims
The authors claim that their results strengthen the robustness of findings regarding dynamical dark energy when combining DESI, CMB, and SNIa data. The primary significance lies in confirming that the preference for dynamical dark energy is driven by a specific feature—a moderate increase in the expansion rate around $z \simeq 0.7$—rather than a broad, model-dependent artifact.

The paper concludes that while the data hints at dynamical dark energy, the signal is currently a modest statistical fluctuation rather than a definitive discovery. The authors emphasize that the low-redshift range ($z \lesssim 0.8$) is the critical region where these hints appear, and future data (particularly additional BAO and SNIa) in this range will be essential to confirm or refute these findings. They explicitly state that their flexible modeling approach does not reveal any new, significant anomalies beyond what the standard $(w_0, w_a)$ analysis suggested, but it does provide a clearer, more granular view of where in redshift space the data deviates from $\Lambda$CDM.