Dark Energy Is Not That Into You: Variable Couplings after DESI DR2 BAO

In interacting dark energy (DE) and dark matter (DM) scenarios, the interaction function typically includes a coupling parameter $\xi$ that quantifies the strength of energy exchange between the dark sectors. While $\xi$ is often assumed to be constant, there is no fundamental reason to exclude a time-dependent coupling, which could provide a more general and realistic description of dark sector dynamics. In this work, we study two widely used interacting models involving pressureless DM and DE, where the coupling parameter is allowed to vary with the scale factor $a$. Specifically, we consider two parametrizations: $\xi(a) = \xi_0 + \xi_a (1-a)$ and $\xi(a) = \xi_0 \left(1 + \frac{1-a}{a^2 + (1-a)^2} \right)$, and constrain them using the latest cosmological observations, including Planck 2018 CMB data, DESI DR2 BAO measurements, and multiple Type Ia supernovae samples. Our results show that one scenario yields evidence for a non-zero interaction at more than 95\% confidence level, while the remaining cases indicate at most mild or inconclusive signs of interaction. These findings highlight the potential of variable coupling models and the importance of continued investigation into the nature of the dark sectors.