Theoretical analysis on the Barrow holographic dark energy in the DGP braneworld

This paper further studies the cosmological evolution and geometry diagnosis of Barrow holographic dark energy (BHDE) in the DGP braneworld, specifically, by choosing the interaction between dark energy and dark matter item. Q(1) = 3Hde, Q(2) = 3Hdm, Q(3) = 3Hde2=(de + dm), Q(4) = 3Hdm2=(de + dm) are discussed in the case of no interaction and four different interactions, the evolution laws of energy density parameters, deceleration parameters and EOS (equation of state) parameters of Barrow holographic dark energy. The results show that the Barrow holographic dark energy in the DGP braneworld conforms to the current cosmic evolution rule, already achieved the universe main ingredients from matter to the transition of energy, and explains the problem of cosmic acceleration. Further, in order to distinguish between the model and CDM model, this paper also geometrically diagnoses the model with the two ways of Statefinder hierarchy and Om(z). From their respective evolution image you can see, these two kinds of diagnosis methods can not only distinguish different from CDM model, but also can intuitively reect the coupling parameters that can significantly affect the dark energy model.