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 $\Lambda$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: $\xi=2.63^{ +0.63}_{ -0.52}$, $\xi + 3w_X = -0.98^{ +1.90}_{ -2.07}$ with the GOLD sample ($1.4\le z \le5.6$) and $\xi=2.83^{ +0.63}_{ -0.58}$, $\xi + 3w_X = 0.03^{ +1.35}_{ -1.33}$ with the FULL sample ($1.4\le z \le8.2$), respectively. Our analysis shows that the $\Lambda$CDM model without interaction ($\xi=3$, $\xi + 3w_X = 0$) is consistent with the latest \emph{ Fermi} sample and DESI DR2 at $1\sigma$ confidence level. We find no significant deviations from the standard model using AIC and BIC criterias.
Categories: astro-ph.CO hep-ph