Cosmological Constraints on the Phenomenological Interacting Dark Energy Model with Fermi Gamma-Ray Bursts and DESI DR2

In this work, we constrain the phenomenological interacting dark energy (IDE) model using \emph{Fermi} gamma-ray burst (GRB) dataset and the latest baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2). Through a joint Bayesian analysis, we perform a cosmological comparative assessment of the $Λ$CDM, $w$CDM, and CPL models with the phenomenological IDE model. For the phenomenological IDE model in a flat universe with \emph{Fermi} samples and DESI DR2, we obtain: $ξ=2.63^{+0.63}_{-0.52}$, $ξ+ 3w_X = -0.98^{+1.90}_{-2.07}$ with the GOLD sample ($1.4\le z \le5.6$) and $ξ=2.83^{+0.63}_{-0.58}$, $ξ+ 3w_X = 0.03^{+1.35}_{-1.33}$ with the FULL sample ($1.4\le z \le8.2$), respectively. Our analysis shows that the $Λ$CDM model without interaction ($ξ=3$, $ξ+ 3w_X = 0$) is consistent with the latest \emph{Fermi} sample and DESI DR2 at $1σ$ confidence level. We find no significant deviations from the standard model using AIC and BIC criterias.