Interacting dark energy constraints from Fermi GRBs and Pantheon+ SNe Ia with full GRB covariance
The standard $Λ$CDM model faces long-standing theoretical and observational problems, such as the Hubble tension, which motivate extensions beyond $Λ$CDM, including interacting dark energy (IDE). Type Ia supernovae (SNe Ia) are precise probes of the late-time expansion history, while gamma-ray bursts (GRBs) can extend the Hubble diagram to higher redshifts. However, GRB cosmology depends on careful calibration and uncertainty modeling. Using an Amati relation calibrated with the corresponding low-redshift GRBs, we construct distance moduli for the high-redshift subsets of the 15-year \textit{Fermi}/GBM GOLD and FULL samples and combine them with Pantheon+ SNe Ia to compare flat $Λ$CDM, $w$CDM, IDE-$ρ_{\rm de}$, and IDE-$ρ_{\rm c}$ models. The covariance of the calibrated Amati intercept and slope is propagated into a full, non-diagonal GRB distance-modulus covariance, and an effective residual scatter, $σ_{\rm res,μ}$, is fitted jointly with the cosmological parameters. The GOLD and FULL samples yield very similar constraints on the main cosmological parameters. With either the full or diagonal GRB covariance, the IDE models do not improve likelihood sufficiently to compensate for their additional parameters, and the BIC favors $Λ$CDM. Removing the Planck prior on $ω_b$ leaves the main cosmological constraints essentially unchanged. A SNe-only comparison shows that the additional constraining power of the GRBs is generally modest. Fixing $σ_{\rm res,μ}=0$ produces unacceptable GRB fits for all four models. Current GRB and Pantheon+ distance measurements provide no significant evidence for either of the two IDE interactions considered here.