Non-linear logarithmic interactions and a varying polytropic gas

In this paper we will demonstrate possible existence of more exotic forms of interaction taking into account, that dark energy can be parametrized as a varying polytropic uid suggested recently by the first author. On going research in both directions, i.e. dark energy and non-gravitational interaction, opens very interesting perspectives for solving the problems which are related to the accelerated expansion of the Universe. The fact that available observational data allows to parametrize the dark side of our Universe in form of interacting dark uids is not less surprising, than the accelerated expansion itself. Therefore, the consideration of new forms of non-gravitational interactions in modern cosmology still is one of the actual topics and requires deep and systematic research. This fact motivates us to consider various new forms of non-gravitational logarithmic interactions and study their cosmological consequences. Appropriate classification of the models is presented in the light of actively discussed Om analysis and the result for the Hubble parameter measured at z = 2:34 in BOSS experiment.