Is dark energy evolving? Robustness, functional form, and model selection for the DESI DR2 + Pantheon+ + cosmic-chronometer preference for dynamical dark energy

Whether the dark-energy equation-of-state parameter $w$ equals the cosmological-constant value $-1$ or evolves with cosmic time is among the most consequential open questions in cosmology, sharpened by the DESI DR2 baryon-acoustic-oscillation report (2025) of a 2.8–4.2$\sigma$ preference for evolving dark energy. A 2026 joint analysis of DESI DR2 BAO, Pantheon+ Type Ia supernovae, and cosmic-chronometer $H(z)$ data finds a $\sim4\sigma$ deviation of $w_0$ from $-1$ in a one-parameter model but only moderate ($>1.5\sigma$) evidence for time evolution from late-time data. This problem asks for a definitive, systematics-controlled determination of whether current combined probes genuinely require dynamical dark energy — and if so, with which redshift dependence — with conclusions demonstrably robust to statistical methodology, dataset combination, and cosmological modeling choices. As of August 2026 the question is actively contested, with published analyses reaching opposite verdicts from overlapping data.

Background

The discovery of cosmic acceleration established that about 70% of the present-day energy density of the Universe is dark energy, a smooth component with negative pressure. Its ratio of pressure to energy density, the equation-of-state parameter $w=p/\rho$, equals $-1$ exactly for a cosmological constant $\Lambda$, which is the assumption underlying the standard flat $\Lambda$CDM cosmological model. Whether $w$ stays at $-1$ or varies with redshift $z$ (dynamical or evolving dark energy) remains one of the central open questions of observational cosmology.

The observational handles are geometric probes of the expansion history: baryon acoustic oscillations (BAO), the sound-horizon scale imprinted in the primordial photon–baryon plasma and frozen into galaxy clustering, which acts as a standard ruler; Type Ia supernovae (SNe), standard candles compiled in the Pantheon+ sample; cosmic chronometers (CC), passively evolving galaxies whose stellar ages date the Universe at different redshifts and thereby give the Hubble parameter $H(z)$ directly; and the cosmic microwave background (CMB), which fixes the early-universe normalization. Departures from $w=-1$ are usually tested with two-parameter phenomenological templates, most commonly the Chevallier–Polarski–Linder (CPL) form $w(a)=w_0+w_a(1-a)$, where $a$ is the scale factor normalized to 1 today. Model comparison between nested and non-nested $w(z)$ forms commonly uses the Akaike and Bayesian information criteria (AIC and BIC), which reward fit quality while penalizing extra parameters in different ways, so the two criteria can rank the same models differently.

In March 2025 the Dark Energy Spectroscopic Instrument (DESI) second data release (DR2) reported that its BAO measurements, combined with CMB and supernova data, prefer evolving dark energy over $\Lambda$CDM at 2.8–4.2$\sigma$, with a best fit in the so-called quintom quadrant $w_0>-1$, $w_a<0$ (an equation of state that is phantom-like, $w<-1$, at early times and rises above $-1$ near the present epoch, crossing the phantom divide in between). Kumari and Kumar (2026) analyzed DESI DR2 BAO together with Pantheon+ and cosmic-chronometer data across several one- and two-parameter templates, finding a $\sim4\sigma$ deviation of the one-parameter $w_0$ from $-1$ but only moderate ($>1.5\sigma$) evidence for time evolution from the late-time data alone — under the modeling assumptions of spatial flatness, negligible late-time radiation, and a fixed sound-horizon prior $r_d=147.09\pm0.20\,\mathrm{Mpc}$. A closely connected benchmark is the $H_0$ tension, the long-standing disagreement between locally measured (~73 km/s/Mpc) and CMB-inferred (~67 km/s/Mpc) values of the present-day Hubble constant, which any successful dynamical-dark-energy explanation would be expected to address or at least not worsen.

Problem Statement

Determine whether the preference for $w\neq-1$ found in combined current late-time data — DESI DR2 BAO, Pantheon+ Type Ia supernovae, and cosmic-chronometer $H(z)$ measurements, with or without early-universe (CMB) constraints — reflects genuinely evolving dark energy, or arises from a statistical fluctuation, prior choice, or residual systematics in one or more of the compilations. As part of the same objective: (i) establish which functional form of $w(z)$, if any, the data actually select among the standard one- and two-parameter templates (CPL and its near-degenerate alternatives), or demonstrate that current data cannot distinguish them; and (ii) determine whether the model-selection verdict between dynamical dark energy and $\Lambda$CDM is stable under changes of information criterion (AIC versus BIC), dataset combination, and the modeling choices of spatial flatness, late-time radiation, and the sound-horizon prior $r_d$. All deliverables jointly serve one overarching objective: a definitive, systematics-controlled verdict on whether current observations require abandoning the cosmological constant, together with the redshift dependence of any confirmed evolution.

References

1. Chanchal Kumari and Dinesh Kumar, 'Probing the Evolution of Dark Energy: A Joint Analysis of DESI DR2, Pantheon+, and Cosmic Chronometers' (2026), arXiv:2604.05849, DOI 10.48550/arxiv.2604.05849, https://arxiv.org/abs/2604.05849
2. DESI Collaboration (M. Abdul-Karim, J. Aguilar, S. Ahlen, et al.), 'DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints' (2025), Phys. Rev. D 112, 083515, DOI 10.1103/tr6y-kpc6, arXiv:2503.14738, https://arxiv.org/abs/2503.14738
3. Samsuzzaman Afroz and Suvodip Mukherjee, 'Hint towards inconsistency between BAO and Supernovae Dataset: The Evidence of Redshift Evolving Dark Energy from DESI DR2 is Absent' (2025), arXiv:2504.16868, https://arxiv.org/abs/2504.16868
4. George Efstathiou, 'Baryon Acoustic Oscillations from a Different Angle' (2025), arXiv:2505.02658, https://arxiv.org/abs/2505.02658
5. Deng Wang and David Mota, 'Did DESI DR2 truly reveal dynamical dark energy?' (2025), arXiv:2504.15222, https://arxiv.org/abs/2504.15222
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