Spacetime Metrology with LISA Pathfinder

TL;DR

LISA Pathfinder aims to test high-precision spacetime metrology by measuring relative acceleration and displacement of free-falling test masses, demonstrating gravitational wave detection techniques in space.

Contribution

The paper introduces a novel approach to calculating Doppler response to gravitational waves and discusses system identification methods for calibrating the LISA Pathfinder instrument.

Findings

Achieved differential acceleration noise of 3×10^{-14} m s^{-2} Hz^{-1/2}

Demonstrated the effectiveness of control logic in noise compensation

Validated system identification procedures with synthetic data

Abstract

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.