Testing the phenomenological interacting dark energy model with gamma-ray bursts and Pantheon+ type Ia supernovae

In this paper, we utilize recent observational data from gamma-ray bursts (GRBs) and Pantheon+ supernovae Ia (SNe Ia) sample to explore the interacting dark energy (IDE) model in a phenomenological scenario. Results from GRBs alone, SNe Ia and GRBs+SNe Ia indicate that the energy is transferred from dark energy to dark matter and the coincidence problem is alleviated. The value of $H_0$ from GRBs+SNe Ia in the IDE scenario shows agreement with the SH0ES measurement. Considering the age estimate of the quasar APM 08279+5255 at $z=3.91$, we find that the phenomenological IDE scenario can predict a cosmic age greater than that of the $\mathrm{\Lambda }$CDM model, thus the cosmic age problem can be alleviated.