Testing general relativity and alternative theories of gravity with space-based atomic clocks and atom interferometers

The successful miniaturisation of extremely accurate atomic clocks and atom interferometers invites prospects for satellite missions to perform precision experiments. We discuss the effects predicted by general relativity and alternative theories of gravity that can be detected by a clock, which orbits the Earth. Our experiment relies on the precise tracking of the spacecraft using its observed tick-rate. The spacecraft's reconstructed four-dimensional trajectory will reveal the nature of gravitational perturbations in Earth's gravitational field, potentially differentiating between different theories of gravity. This mission can measure multiple relativistic effects all during the course of a single experiment, and constrain the Parametrized Post-Newtonian Parameters around the Earth. A satellite carrying a clock of fractional timing inaccuracy of $\Delta f/f \sim 10^{-16}$ in an elliptic orbit around the Earth would constrain the PPN parameters $|\beta -1|, |\gamma-1| \lesssim 10^{-6}$. We also briefly review potential constraints by atom interferometers on scalar tensor theories and in particular on Chameleon and dilaton models