Robustness and physical interpretation of the evolving dark energy preference in DESI-era data: shared SN/BAO systematics, prior and parametrization sensitivity, microphysical mapping, and the predicted flattening of the growth rate $f\sigma_8(z)$

Keeley, Abazajian, Kaplinghat and Shafieloo (Phys. Rev. D 112, 043501, 2025) fitted a flexible 'transitional dark energy' (TDE) parametrization of the dark energy equation of state to Planck CMB + DESI BAO + supernova data and found a 2.4–3.8 sigma preference for evolving dark energy over the cosmological constant, along with a predicted flattening of the growth-rate curve $f\sigma_8(z)$. The paper leaves open five linked issues: whether unrecognized systematic errors shared across independent SN and BAO surveys could remove the preference; whether the inference is prior- or parametrization-driven; whether the preferred expansion histories can be mapped onto viable microphysical models; whether nonlinear, scale-dependent, or modified-gravity effects change the predicted redshift-space-distortion signatures; and whether a joint end-to-end systematic error characterization can secure the inference. Through August 2026, all five threads remain actively contested and none is resolved.

Background

The concordance cosmological model, $\Lambda$CDM, explains the observed accelerating expansion with a cosmological constant $\Lambda$: a dark energy component whose density is constant in time and whose equation of state (the ratio of pressure to energy density) is $w=-1$. The Dark Energy Spectroscopic Instrument (DESI), which measures baryon acoustic oscillations (BAO — a standard-ruler length scale imprinted on galaxy clustering, set by sound waves in the pre-recombination plasma) in millions of galaxies and quasars, reported in 2024–2025 that its BAO distances, combined with cosmic microwave background (CMB) data and Type Ia supernova (SN) compilations, prefer a time-evolving equation of state $w(z)$ over $w=-1$ at roughly $2.5$–$4\sigma$, depending on the SN sample. Most analyses use the Chevallier–Polarski–Linder (CPL) parametrization, a linear ansatz $w(a)=w_0+w_a(1-a)$ in the scale factor $a$; a known concern is that flexible parametrizations can generate spurious evidence through prior-volume effects, because Bayes factors between non-nested models depend on how parameter space volume is weighted. Keeley, Abazajian, Kaplinghat and Shafieloo (2025) instead used the 'transitional dark energy' (TDE) parametrization, which permits rapid transitions in $w(z)$ at a transition redshift $z_t$ of width $\Delta z$, with priors $0\le z_t,\Delta z\le 10$; they found a $3.8\sigma$ preference with the 5-year Dark Energy Survey (DES) SN sample and $2.4\sigma$ with Pantheon+ (PP), corroborating the DESI Collaboration's CPL-based result. Notably, the same modification to the expansion history near $0.25<z<0.75$ improves the fits of both the SN and BAO datasets, so a systematic explanation would require shared systematics across statistically independent surveys. The reconstructed histories prefer $w(z)>-1$ (quintessence-like: compatible with a canonical scalar field, for which $w\ge-1$) at $z\lesssim 0.5$ and $w$ close to or below $-1$ (phantom-like: $w<-1$, not achievable by a canonical scalar field) at $z>0.5$; the TDE ansatz enforces positive dark energy density and therefore may not capture rolling scalar fields with a negative cosmological constant or interacting dark sectors. The paper also derives an approximate analytic relation (its Eq. 10) linking fractional changes in the expansion rate $H(z)$ to changes in the growth-rate observable $f\sigma_8$ — the product of the logarithmic growth rate of matter perturbations, $f=d\ln\delta_m/d\ln a$, and $\sigma_8$, the rms matter fluctuation on $8\,h^{-1}$Mpc scales, measurable from redshift-space distortions (RSD, the anisotropic apparent clustering caused by galaxies' peculiar velocities) — accurate to about 3% in the linear regime, predicting a characteristic flattening of the $f\sigma_8(z)$ curve relative to $\Lambda$CDM that upcoming DESI RSD data could test. Recent developments include the DESI Data Release 2 (DR2) BAO measurements (2025), which found the preference persisting at $3.1\sigma$ for BAO+CMB and $2.8$–$4.2\sigma$ when SNe are added; Efstathiou's (2024) argument that a $\sim0.04$ mag offset between the DES and Pantheon+ SN compilations could reconcile the data with $\Lambda$CDM; the DES Collaboration's recalibrated DES-Dovekie SN reanalysis (2025), which reduced the DES-based significance from $4.2\sigma$ to $3.2\sigma$; nonparametric Gaussian-process reconstructions that find the preference strongly analysis-dependent; and growth-based tests using DESI full-shape galaxy clustering that are as yet inconclusive.

Problem Statement

For the evolving-dark-energy preference established with the transitional dark energy (TDE) parametrization in combined CMB + DESI BAO + supernova data (Keeley, Abazajian, Kaplinghat & Shafieloo, Phys. Rev. D 112, 043501): determine whether it reflects genuine new physics rather than analysis artifacts, and what it implies physically, by resolving the linked open issues the source itself identifies (its first and fifth issues — shared systematics and a joint end-to-end systematic error characterization — are treated together in component (1) below). (1) Diagnose and quantify whether unrecognized systematic errors — including photometric and flux calibration, supernova population and dust modeling, covariance-matrix estimation, and BAO modeling choices — shared or unshared across the independent SN compilations and DESI BAO measurements can reduce or eliminate the preference, including a joint end-to-end systematic error characterization of DESI and modern SN compilations. (2) Establish how sensitive the inferred preference and posterior shapes are to prior choices and to the parametrization of $w(z)$, controlling prior-volume effects in the model comparison against $\Lambda$CDM. (3) Map the preferred expansion histories ($w(z)>-1$ at $z\lesssim0.5$ crossing to $w\lesssim-1$ at higher redshift, with a transition near $z\sim0.5$) onto concrete microphysical models — such as canonical rolling scalar fields, models with negative cosmological constant, and interacting dark sectors, the last two being classes the positive-density TDE ansatz may not capture — and assess the viability (stability, consistency with constraints) of the resulting models. (4) Determine, beyond the $\sim3\%$-accurate linear general-relativistic relation between $\delta H/H$ and $\delta(f\sigma_8)/f\sigma_8$, how all of the following alter the predicted flattening of the $f\sigma_8(z)$ curve — non-linear structure growth, scale dependence, and possible modified-gravity effects ($G_{\mathrm{eff}}(a)\neq G_N$) — and whether current and near-future DESI redshift-space-distortion data confirm or exclude that signature. These components jointly serve one objective: a defensible verdict on whether the DESI-era preference for evolving dark energy is real, and what it means for the microphysical nature of dark energy. For (1) determine which of the listed systematic categories can and cannot account for the preference; for (2) which prior and parametrization choices preserve and which remove it; for (3) which of the listed model classes do and do not admit the preferred expansion histories; and for (4) how each named effect alters the predicted flattening and which effects remain untreated. The near-future DESI redshift-space-distortion measurements in component (4) are not yet available, so that clause is to be met by a forecast of the predicted signature rather than by a determination from data.

References

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