Mimicking Phantom Dark Energy with Evolving Dark Matter Mass

We present a general method to reproduce a given cosmological background through energy exchange between dark energy (DE) and dark matter (DM). This can be simply realized with a standard quintessence scalar field that controls the DM mass. In particular a background with phantom crossing can be effectively realized without introducing ghosts or other pathologies. For example one can reproduce exactly the background that gives the best fit to the recent DESI+CMB+DESY5 data, within the Chevallier-Polarski-Linder (CPL) parametrization of DE. Although the background evolution is identical, the perturbations differ, leading to modified growth of structures. If the DM mass varies at late times, early-time observables are not modified and can reproduce the main predictions of the target model, but late-time observables are affected. We discuss in particular the effects on the matter power spectrum, CMB lensing and ISW effect. When reproducing the best fit CPL background model, this scenario generically predicts $\mathcal{O}(10\%)$ deviations in such observables. However, for suitable choices of parameters, effects on the matter power spectrum can be smaller, motivating a detailed study. In general, energy exchange between DE and DM generates a mismatch between the matter power spectrum and the gravitational potential amplitudes compared to the decoupled case, that can lead to deviations observable in future experiments.