Spacetime metrology with LISA Pathfinder

LISA is the proposed ESA-NASA space-based gravitational wave detector in the 0.1 mHz - 0.1 Hz band. LISA Pathfinder is the down-scaled version of a single LISA arm. In this thesis it is shown that the arm -- named Doppler link -- can be treated as a differential accelerometer, measuring the relative acceleration between test masses. LISA Pathfinder -- the in-flight test of the LISA instrumentation -- is currently in the final implementation and planned to be launched in 2014. It will set stringent constraints, with unprecedented pureness, on the ability to put test masses in geodesic motion to within the required differential acceleration of 3\times10^{-14} m s^{-2} Hz^{-1/2} and track their relative motion to within the required differential displacement measurement noise of 9\times10^{-12} m Hz^{-1/2}, at frequencies relevant for the detection of gravitational waves. Given the scientific objectives, it will carry out -- for the first time with such high accuracy required for gravitational wave detection -- the science of spacetime metrology, in which the Doppler link between two free-falling test masses measures the spacetime curvature. This thesis contains a novel approach to the calculation of the Doppler response to gravitational waves. It shows that the parallel transport of 4-vectors records the history of gravitational wave signals passing through photons exchanged between an emitter and a receiver. In practice, the Doppler link is implemented with 4 bodies (two test masses and two spacecrafts) in LISA and 3 bodies (two test masses within a spacecraft) in LISA Pathfinder. Different non-idealities may originate in the measurement process and noise sources couple the motion of the test masses with that of the spacecraft. To compensate for such disturbances and stabilize the system a control logic is implemented during the measurement. The complex closed-loop dynamics of LISA Pathfinder can be condensed into operators acting on the physical coordinates describing the relative motion. The formalism can handle the couplings between the test masses and the spacecraft, the sensing noise, as well as the cross-talk, and allows for the system calibration. It suppresses the transients in the estimated residual acceleration noise between the test masses. The scope of system identification is indeed the calibration of the instrument and the compensation of different effects. After introducing a model for LISA Pathfinder along the optical axis and an example of cross-talk from other degrees of freedom to the optical axis, this thesis describes some data analysis procedures applied to synthetic experiments and tested on a realistic simulator provided by ESA. The same procedures will also be adopted during the mission. Those identification experiments can also be optimized to get an improvement in precision of the noise parameters that the performances of the mission depend on. This thesis demonstrates the fundamental relevance of system identification for the success of LISA Pathfinder in demonstrating the principles of spacetime metrology needed for all future space-based missions.