## Spacetime Metrology with LISA Pathfinder

by **Congedo, Giuseppe**

PhD thesis defended at University of Trento on 26th March 2012. Advisors: Stefano Vitale, Mauro Hueller. Committee: Eugenio Coccia (Univ. of Rome, Tor Vergata), Philippe Jetzer (Univ. of Z\”urich), Eric Plagnol (APC-CNRS, Paris), Rita Dolesi (Univ. Of Trento)

LISA is the proposed ESA-NASA gravitational wave detector in the 0.1 mHz – 0.1 Hz band. LISA Pathfinder is the down-scaled version of a single LISA arm. 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 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}, around 1 mHz. 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 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. In practice, the Doppler link is implemented with 4 bodies in LISA and 3 bodies in LISA Pathfinder. To compensate for noise sources a control logic is implemented during the measurement. The closed-loop dynamics of LISA Pathfinder can be condensed into operators acting on the motion coordinates, handling the couplings, as well as the cross-talks. The scope of system identification is the optimal calibration of the instrument. This thesis describes some data analysis procedures applied to synthetic experiments and shows the relevance of system identification for the success of LISA Pathfinder in demonstrating the principles of spacetime metrology for all future space-based missions.