Free-floating planets are recently drawing a special interest of thescientific community. Gravitational microlensing is up to now the exclusivemethod for the investigation of free-floating planets, including their spatialdistribution function and mass function. In this work, we examine thepossibility that the future Euclid space-based observatory may allow todiscover a substantial number of microlensing events caused by free-floatingplanets. Based on latest results about the free-floating planet mass functionin the mass range $[10^{-5}, 10^{-2}]M_{\odot}$, we calculate the optical depthtowards the Galactic bulge as well as the expected microlensing rate and findthat Euclid may be able to detect hundreds to thousands of these events permonth. Making use of a synthetic population, we also investigate thepossibility of detecting parallax effect in simulated microlensing events dueto free-floating planets and find a significant efficiency for the parallaxdetection that turns out to be around 30%.
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