Statefinder diagnosis for holographic dark energy in the DGP braneworld

Many dark energy (DE) models have been proposed, in recent years, to explain the acceleration of the expansion of the Universe. It seems necessary to differentiate the various DE models in order to check the viability of each model. The statefinder diagnostic is a useful method to accomplish this. In this paper, we investigate the statefinder diagnosis parameters for the holographic dark energy (HDE) model in two cosmological setups. First, we study the statefinder diagnosis for HDE in the context of a flat Friedmann-Robertson-Walker Universe in Einstein gravity. Then, we extend our study to the Dvali-Gabadadze-Porrati braneworld framework. For the system’s IR cutoff we choose the Hubble radius and the Granda-Oliveros cutoff inspired by the Ricci scalar curvature. We plot the evolution of statefinder parameters $\{r,s\}$ in terms of the redshift parameter $z$. We also compare the results with those obtained for statefinder diagnosis parameters of other DE models, in particular the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 1

The evolution of ${\mathrm{\Omega }}_D$ versus the redshift parameter $z$ for HDE with the GO cutoff in standard cosmology. Left panel: $\alpha <1$; right panel: $\alpha >1$.

Figure 2

The evolution of ${\omega }_D$ versus the redshift parameter $z$ for HDE with the GO cutoff in standard cosmology. Left panel: $\alpha <1$; right panel: $\alpha >1$.

Figure 3

The evolution of the deceleration parameter $q$ against the redshift parameter $z$ for HDE with the GO cutoff in standard cosmology.

Figure 4

The evolution of the statefinder parameter $r$ versus the redshift parameter $z$ for $\alpha <1$ (left panel) and $\alpha >1$ (right panel).

Figure 5

The evolution of the statefinder parameter $r$ versus the deceleration parameter $q$ for $\alpha <1$ (left panel) and $\alpha >1$ (right panel).

Figure 6

The evolution of $w_D$ and the deceleration parameter $q$ versus the redshift parameter $z$ for the two branches of the DGP braneworld. For both cases, $(\epsilon =1,c<1)$ and $(\epsilon =-1,c>1)$, the diagrams are quite similar to each other.

Figure 7

The evolution of $w_D$ versus the redshift parameter $z$ for HDE with the GO cutoff in the DGP braneworld. Left panel corresponds to $\alpha <1$ and $\beta <0$; right panel corresponds to $\alpha >1$ and $\beta >0$.

Figure 8

The evolution of the deceleration parameter $q$ versus the redshift parameter $z$ for HDE with the GO cutoff in the DGP braneworld. Left panel corresponds to $\alpha <1$ and $\beta <0$; right panel corresponds to $\alpha >1$ and $\beta >0$.

Figure 9

The evolution of the statefinder parameter $r$ versus $1+z$ for HDE with the GO cutoff in the DGP braneworld.

Figure 10

The evolution of the statefinder parameter $s$ versus $1+z$ for HDE with the GO cutoff in the DGP braneworld.

Figure 11

The evolution of the statefinder parameter $r$ versus the deceleration parameter $q$ for HDE with the GO cutoff in the DGP braneworld.

Figure 12

The evolution of the statefinder parameter $r$ versus $s$ for HDE with the GO cutoff in the DGP braneworld.