Theoretical Analysis on QCD Ghost Dark Energy in the DGP Braneworld

We study the evolution of a QCD ghost dark energy model under two branches of the DGP braneworld, and this model is distinguished from the $$\Lambda$$ CDM model by diagnostic methods of Statefinder hierarchy and Om( $$z$$ ). Through the derivation of the evolution equation of the energy density parameters, the deceleration parameters and the equation-of-state (EoS) parameter, it can be proved that in both noninteractive and interactive scenarios (specifically, including $$Q_{1}=3H\xi\rho_{\textrm{de}},Q_{2}=3H\xi\rho_{\textrm{dm}},Q_{3}=3H\xi(\rho_{\textrm{de}}+\rho_{\textrm{dm}})$$ ), this model can well describe the evolution rule of today’s universe. In the later stage of the evolution of the universe, the main component of the universe changed from dark matter to dark energy, and the universe gradually transitioned from decelerating expansion to accelerating expansion, and it will not end up with a big rip in the future. And in the self-accelerating branch of the DGP braneworld, the accelerated expansion of the universe occurred earlier. In order to distinguish the QCD model from the $$\Lambda$$ CDM model, we adopted two diagnostic methods, namely, the Statefinder diagnostic and the Om diagnostic. From their respective diagnostic images, it can be seen that these two diagnostic methods cannot only effectively distinguish the QCD model from $$\Lambda$$ CDM, but also directly reflect that the coupling parameters $$\xi$$ have a certain impact on the dark energy model. It can also eliminate the degeneracy of different coupling parameters under the same interaction.