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The third data release (DR3) of the European Space Agency satellite Gaiaprovides coordinates, parallaxes, proper motions, and radial velocities for asample of $\sim 34$ million stars. We use the combined 6-dimensional phasespace information to search for hypervelocity stars (HVSs), unbound starsaccelerated by dynamical processes happening in the Galactic Centre. By lookingat the kinematics of Gaia DR3 stars in Galactocentric coordinates and byintegrating their orbits in the Galactic potential, we do not identify any HVScandidates with a velocity higher than $700$ km s$^{-1}$ and robustly observedkinematics. Assuming a scenario wherein the interaction between a stellarbinary and the massive black hole Sgr A$^*$ is responsible for HVS ejectionsfrom the Galactic Centre, we derive degenerate limits on the ejection rate ofHVSs and the slope of the initial mass function of the primary star amongbinaries in the Galactic Centre. Our results indicate that the HVS ejectionrate is $\lesssim 8\times10^{-5}$ yr$^{-1}$ assuming a Salpeter mass function,and this upper limit becomes progressively smaller for an increasinglytop-heavy mass distribution. A fiducial HVS ejection rate of $10^{-4}$yr$^{-1}$ prefers a mass function slope $\lesssim -2.35$, disfavouringpreviously claimed top-heavy initial mass functions among stars in the GalacticCentre.

Gaia DR3 in 6D: The search for fast hypervelocity stars and constraints on the Galactic Centre environment