Holographic dark energy with time depend gravitational constant in the non-flat Ho$\check{r}$ava-Lifshitz cosmology

Understand

We study the holographic dark energy on the subject of Ho$\check{r}$ava-Lifshitz gravity with a time dependent gravitational constant (G(t)), in the non-flat space-time.

• We obtain the differential equation that specify the evolution of the dark energy density parameter based on varying gravitational constant.
• we find out a relation for the state parameter of the dark energy equation to low redshifts which containing varying $G$ correction.