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

Abstract: 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, we obtain: $ξ=2.644^{+1.144}_{-0.933}$, $ξ+ 3w_X = -1.001^{+2.827}_{-3.153}$ with the GOLD sample ($z \geq 1.4$) and DESI DR2; and $ξ=2.879^{+0.995}_{-0.990}$, $ξ+ 3w_X = 0.086^{+1.365}_{-1.440}$ with the FULL sample ($z \geq 1.4$) and DESI DR2. Our analysis shows that the $Λ$CDM model without interaction are consistent with the latest \emph{Fermi} sample and DESI DR2 at $1σ$ confidence level.