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The theory of general relativity describes macroscopic phenomena driven bythe influence of gravity while quantum mechanics brilliantly accounts formicroscopic effects. Despite their tremendous individual success, a completeunification of fundamental interactions is missing and remains one of the mostchallenging and important quests in modern theoretical physics. The STE-QUESTsatellite mission, proposed as a medium-size mission within the Cosmic Visionprogram of the European Space Agency (ESA), aims for testing general relativitywith high precision in two experiments by performing a measurement of thegravitational 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 inthe gravitational field of Earth comparing the trajectory of two Bose-Einsteincondensates of Rb85 and Rb87. The two ultracold atom clouds are monitored veryprecisely thanks to techniques of atom interferometry. This allows to reachdown to an uncertainty in the E\"otv\"os parameter of at least 2x10E-15. Inthis paper, we report about the results of the phase A mission study of theatom interferometer instrument covering the description of the main payloadelements, the atomic source concept, and the systematic error sources.

STE-QUEST - Test of the Universality of Free Fall Using Cold Atom Interferometry