We have just published on https://arxiv.org/abs/1908.11785 a white paper on the scientific motivation for future space tests of the equivalence principle, to explore some of the big questions in physics (e.g. Equivalence Principle, Dark Matter and Gravitational Waves) using matter-wave interferometry, especially in space.
We discuss two possible mission scenarios, one based on quantum technologies, the other on electrostatic accelerometers, that could reach that goal are briefly discussed. We propose experiments to test the universality of free fall, at the level of 10−17 or better.