Correspondence between a decaying dark matter sector scenario and scalar field model

Abstract

We explore the theoretical viability of modeling a decaying dark matter sector through a unified scalar field approach. Using exact analytical solutions of the Friedmann constraints, we map the fluid phenomenology onto a scalar field potential. Our analysis reveals that physical viability, specifically the existence of a well-defined potential minimum; inevitably forces the dark energy equation of state into the phantom domain. To resolve the kinetic pathologies at late times, we propose reinterpreting the framework within a complex scenario, mapping the imaginary transition to the angular dynamics of a $U(1)$ phase. This mapping naturally yields an ultra-light mass scale of $m_\phi \sim 10^{-33} \ \text{eV}$, classifying the model as a unified dark fluid. Finally, we employ a dynamical approach to study the effects of non-minimal coupling, proving that the phantom-dominated epoch acts as a stable, late-time cosmic attractor in this kind of cosmological scenario.