Forecasts for interacting dark energy with time-dependent momentum exchange

Models of interacting dark energy and dark matter offer a possible solution to cosmological tensions. In this work, we examine a pure momentum-exchange model with a time-dependent coupling strength $\xi (z)$ that could help to alleviate the $S_8$ tension. We perform Fisher forecasting and MCMC analysis to constrain the coupling strength of this interaction for different redshift bins $0.0<z<2.1$, using the specifications of upcoming DESI-like surveys. For this analysis, we examine both a model with a constant equation of state $w=-0.9$, as well as a thawing dark energy model with an evolving $w(z)$. We show that, for a constant equation of state, $\xi (z)$ can be well constrained in all redshift bins. However, due to a weaker effect at early times, the constraints are significantly reduced at high redshifts in the case of a thawing $w(z)$ model.