Secular gravity gradients in non-dynamical Chern–Simons modified gravity for satellite gradiometry measurements

With continuous advances in related technologies, precision tests of modern gravitational theories with orbiting gradiometers becomes feasible, which may naturally be incorporated into future satellite gravity missions. In this work, we derive, at the post-Newtonian level, the new secular gravity gradient signals from the non-dynamical Chern–Simons modified gravity for satellite gradiometry measurements, which may be exploited to improve the constraints on the mass scale \(M_{CS}\) or the corresponding length scale \({\dot{\theta }}\) of the theory with future missions. For orbiting superconducting gradiometers, a bound \(M_{CS}\ge 10^{-7}\ \mathrm{eV}\) and \({\dot{\theta }} \le 1\ \mathrm{m}\) could in principle be obtained, and for gradiometers with optical readout based on the similar technologies established in the LISA PathFinder mission, an even stronger bound \(M_{CS}\ge 10^{-6}\)–\(10^{-5}\ \mathrm{eV}\) and \({\dot{\theta }} \le 10^{-1}\)–\(10^{-2} \ \mathrm{m}\) might be expected.