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The future space-borne detectors will provide the possibility to detectgravitational waves emitted from extreme mass ratio inspirals of stellar-masscompact objects into supermassive black holes. It is natural to expect that thespin of the compact object and cosmological constant will affect the orbit ofthe inspiral process and hence lead to the considerable phase shift of thecorresponding gravitational waves. In this paper, we investigate the motion ofa spinning test particle in the spinning black hole background with acosmological constant and give the order of motion deviation induced by theparticle's spin and the cosmological constant by considering the correspondinginnermost stable circular orbit. By taking the neutron star or kerr black holeas the small body, the deviations of the innermost stable circular orbitparameters induced by the particle's spin and cosmological constant are given.Our results show that the deviation induced by particle's spin is much largerthan that induced by cosmological constant when the test particle locates notvery far away from the black hole, the accumulation of phase shift during theinspiral from the cosmological constant can be ignored when compared to the oneinduced by the particle's spin. However when the test particle locates very faraway from the black hole, the impact from the cosmological constant willincrease dramatically. Therefore the accumulation of phase shift for the wholeprocess of inspiral induced by the cosmological constant and the particle'sspin should be handled with caution.

Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system