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The Eddington-inspired-Born-Infeld (EiBI) theory has been recentlyresurrected. Such a theory is characterized by being equivalent to Einsteintheory in vacuum but differing from it in the presence of matter. One of thevirtues of the theory is to avoid the Big Bang singularity for a radiationfilled universe. In this paper, we analyze singularity avoidance in this kindof model. More precisely, we analyze the behavior of a homogeneous andisotropic universe filled with phantom energy in addition to the dark andbaryonic matter. Unlike the Big Bang singularity that can be avoided in thiskind of model through a bounce or a loitering effect on the physical metric, wefind that the Big Rip singularity is unavoidable in the EiBI phantom model eventhough it can be postponed towards a slightly further future cosmic time ascompared with the same singularity in other models based on the standardgeneral relativity and with the same matter content described above.

Is Eddington-Born-Infeld theory really free of cosmological singularities?