Eddington-inspired Born-Infeld Gravity with Varying Cosmological Constant

Abstract: In this paper we modify the EiBI model to realize a varying cosmological constant which is determined by matter distribution. We find that the Newton's constant is also variable and its change is related to the change of cosmological constant. And then we study its cosmological behavior. We find that the early universe will have different behaviors if we take different forms of pending functions. And we can avoid singularity in early universe just like the original EiBI model.