We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2±0.1  fm s^{-2}/sqrt[Hz], or (0.54±0.01)×10^{-15}  g/sqrt[Hz], with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8±0.3)  fm/sqrt[Hz], about 2 orders of magnitude better than requirements. At f≤0.5  mHz we observe a low-frequency tail that stays below 12  fm s^{-2}/sqrt[Hz] down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

We describe analytical and numerical methods for calculating forces between conductors due to variations of electrostatic surface potential across their surfaces. In the simple case where the spatial variation of surface potential gives rise to uniform power spectra, we show that the electrostatic force can be large in comparison with, and scale in approximately the same way with distance of closest approach as, the Casimir force. Patch potentials that are consistent with existing experimental data could give rise to forces with a magnitude of 4% of the Casimir force at separations of 0.1 microm.

The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The STE-QUEST satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the Universality of Free Fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose-Einstein condensates of 85 Rb and 87 Rb. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the Eötvös parameter of at least 2 · 10 −15 . In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources.

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