Kalantari & Rahvar (2025) forward-modeled the observed T90T_{90} duration histogram of 1347 Swift/BAT long gamma-ray bursts (LGRBs) through a Monte-Carlo pipeline that fixes the intrinsic burst rate R(z)R(z), a broken-power-law luminosity function ϕ(L)\phi(L), and the detector triggering efficiency η(P)\eta(P) at single published calibrations, and fit the dark-energy equation of state ω(z)=−1+αz\omega(z) = -1 + \alpha z by χ2\chi^2 minimization, obtaining α=0.08−0.02+0.04\alpha = 0.08^{+0.04}_{-0.02}, a reported mild preference for evolving dark energy over the constant-dark-energy Λ\LambdaCDM model. Independent 2014-2026 literature shows that each fixed input is uncertain or contested: the LGRB luminosity function requires redshift evolution, the burst-rate/metallicity mapping is actively debated, detector trigger selection is known to distort duration measures, a rest-frame duration/redshift anti-correlation has been reported, and current fits to baryon-acoustic-oscillation (BAO), cosmic-microwave-background (CMB), and supernova data prefer evolving dark energy in the direction excluded by the source analysis's scan range α∈[0,1]\alpha \in [0,1]. The open problem is to determine, by treating these astrophysical and instrumental inputs and alternative ω(z)\omega(z) parameterizations as sources of systematic uncertainty, whether the duration-histogram preference for evolving dark energy survives as a robust measurement or is attributable to the fixed assumptions.

Background

Gamma-ray bursts (GRBs) are the most luminous electromagnetic transients in the universe; their prompt emission is conventionally characterized by T90T_{90}, the time interval containing 90% of the detected gamma-ray fluence. Bursts with T90>2T_{90} > 2 s ("long" GRBs, LGRBs) arise from the core collapse of massive, rapidly rotating stars (the collapsar scenario), and have been observed out to redshift z≈9z \approx 9, far beyond the reach of Type Ia supernovae. In an expanding universe every source-frame time scale is stretched by the factor 1+z1+z (cosmological time dilation), so the statistical distribution of observed durations carries, in principle, a record of the expansion history. Dark energy is characterized by its equation of state P=ω(z)ρP = \omega(z)\rho relating pressure to energy density: the concordance Λ\LambdaCDM model — cold dark matter plus a cosmological constant Λ\Lambda — has constant ω=−1\omega = -1, while simple extensions let ω\omega evolve with redshift, for example the one-parameter form ω(z)=−1+αz\omega(z) = -1 + \alpha z used in the source analysis, or the two-parameter CPL (Chevallier-Polarski-Linder) form ω(z)=w0+waz/(1+z)\omega(z) = w_0 + w_a z/(1+z).

Most GRB cosmology instead tries to standardize GRB luminosities through empirical correlations and extend the supernova Hubble diagram to high redshift; that route is limited by the absence of low-redshift calibrators and by evidence that some correlations evolve with redshift. Kalantari & Rahvar (2025) proposed a route that avoids standardizable candles entirely: forward-modeling the observed T90T_{90} histogram of 1347 LGRBs detected by the Burst Alert Telescope (BAT) on the Neil Gehrels Swift Observatory. Their pipeline combines: (i) an intrinsic comoving rate R(z)R(z) — the burst rate per comoving volume per source-frame time, taken as the Wanderman & Piran (2010) broken power law in (1+z)(1+z) peaking at z∗=3.6z_* = 3.6; (ii) a broken-power-law peak luminosity function ϕ(L)\phi(L) with break L∗=1052.05L_* = 10^{52.05} erg/s, likewise from Wanderman & Piran (2010) with parameters as fitted by Lien et al. (2014); (iii) a BAT triggering efficiency η(P)\eta(P) — the probability that a burst of observed peak energy flux PP triggers the detector — in the analytic form of Howell et al. (2014), derived from the trigger simulations of Lien et al. (2014); and (iv) a rest-frame duration distribution built from the 385 archive LGRBs with measured redshifts, whose rest-frame durations τ0=T90/(1+z)\tau_0 = T_{90}/(1+z) are treated as statistically independent of redshift (correlation coefficient c=−0.09c = -0.09 in that sample). For an assumed cosmology the detection-weighted redshift distribution is computed, 1347 mock redshifts and rest-frame durations are drawn, mock histograms of T90=τ0(1+z)T_{90} = \tau_0(1+z) are formed, and α\alpha is fit by χ2\chi^2 minimization against the observed histogram, scanning only α∈[0,1]\alpha \in [0, 1]. The result, α=0.08−0.02+0.04\alpha = 0.08^{+0.04}_{-0.02}, was reported as a mild preference for evolving dark energy over Λ\LambdaCDM.

Every ingredient of this inference is held fixed at one published calibration, and each is questionable on independent evidence. The luminosity function is now known to evolve: Qu et al. (2025) exclude the no-evolution form for Type II GRBs (the physically defined long/collapsar class) and require luminosity or density evolution. The mapping of the burst rate onto the cosmic star-formation history, and its dependence on progenitor metallicity (the abundance of elements heavier than helium relative to solar), remain actively debated (Khatiya et al. 2025; Disberg et al. 2025, who find a near-solar metallicity threshold of roughly 0.6Z⊙0.6 Z_\odot for LGRB formation, in tension with the stronger metallicity suppression implicitly encoded in the Wanderman-Piran rate). The assumed independence of τ0\tau_0 and zz is contested: Lloyd-Ronning et al. (2023) report a rest-frame duration/redshift anti-correlation for LGRBs with a proposed metallicity origin, while Horvath et al. (2022) find no significant duration/redshift dependence beyond the short-GRB region. Instrument selection is a documented hazard for duration-based inference: Littlejohns & Butler (2014) showed that duration measures of Swift GRBs are shaped by observer-frame trigger censorship, which alone reduces the significance of cosmological time-dilation signatures in durations to below 2σ2\sigma. Finally, current baryon-acoustic-oscillation (BAO) and cosmic-microwave-background (CMB) data combined with supernovae (DESI Collaboration 2025) prefer evolving dark energy with w0>−1w_0 > -1 and wa<0w_a < 0 — i.e. ω\omega below −1-1 at high redshift, at 2.8-4.2σ\sigma depending on the supernova sample — a direction corresponding to α<0\alpha < 0 that the source analysis never scanned, and no penalized comparison with alternative parameterizations was performed.

Problem Statement

Determine whether the preference for evolving dark energy derived from the Swift LGRB duration histogram is robust. Concretely: quantify how the inferred α\alpha in ω(z)=−1+αz\omega(z) = -1 + \alpha z — and the statistical preference of this evolving-ω\omega (ω\omegaCDM) fit over the constant-ω\omega Λ\LambdaCDM model — changes when the previously fixed inputs of the forward model are treated as sources of systematic uncertainty: (1) the intrinsic rate R(z)R(z) and luminosity function ϕ(L)\phi(L), including the luminosity- and density-evolution variants now favored by independent fits, treated as uncertain rather than fixed; (2) the BAT triggering-efficiency model η(P)\eta(P), varied within plausible instrumental systematics; (3) the dark-energy parametrization itself, extending or replacing the linear ω(z)=−1+αz\omega(z) = -1 + \alpha z (which the source analysis scanned only over α∈[0,1]\alpha \in [0,1]) with alternatives such as the CPL form and α\alpha of either sign; (4) the redshift-known sample (385 bursts) and its selection biases, including enlarged or reweighted redshift-known samples; and (5) the assumed statistical independence of the rest-frame duration τ0\tau_0 and redshift, relaxed to accommodate the duration-redshift anti-correlation reported in the literature. These five analyses jointly serve one objective — establishing whether the duration histogram constitutes a genuine cosmological measurement rather than a reflection of its population and instrument inputs — and they are interdependent through the shared forward model: for example, luminosity-function evolution changes the detection-weighted redshift distribution that the same Monte-Carlo uses to generate the mock durations. Each variation is to be reported separately and in joint combination, with the range or construction adopted for it stated: a single variation that removes the α=0\alpha = 0 exclusion or the ω\omegaCDM-over-Λ\LambdaCDM preference establishes non-robustness, while establishing robustness requires the joint variation of all five inputs to leave the preference intact. The goal is to determine, with quantified systematic uncertainty, whether the α≠0\alpha \neq 0 preference (or any preference of evolving dark energy over Λ\LambdaCDM from this observable) survives these variations, or is instead attributable to the fixed astrophysical and instrumental assumptions.

References

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