LISA Pathfinder noise performance results: disturbances in the sub-mHz frequency band and projection to LISA

The LISA Pathfinder ESA mission was concluded on July 18th, 2017, after 18 months of operations as one of the most successful ESA missions ever. It was launched on December 3rd, 2015 with the purpose of assessing the feasibility of geodesic motion of two free-falling test masses at the level required by LISA, the first space-based gravitational wave observatory programmed for launch in 2034. This was achieved by measuring the relative acceleration between free-falling test masses with a sensitivity several {orders of magnitude} better than any other present or future mission. In addition to this, LISA Pathfinder constituted an advanced technological test for the flight hardware of the LISA mission. In this thesis work I will illustrate the detail of the experimental results obtained in the course of the mission, whose best performance was published in February 2018, and discuss their consequences for LISA. I will, in particular, describe in some detail a series of observations for which a definitive physical model is still lacking. I will then discuss possible explanations with the aim to reduce the number of available interpretations, and in order to lay the basis for a feasible on-ground experimental campaign in view of LISA.