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

TL;DR

This paper investigates holographic dark energy within non-flat Hořava-Lifshitz cosmology considering a time-varying gravitational constant, deriving evolution equations and relations for dark energy parameters with G(t) corrections.

Contribution

It introduces a model of holographic dark energy in Hořava-Lifshitz gravity with a dynamic G, deriving new evolution equations and relations for dark energy parameters.

Findings

Derived differential equation for dark energy density evolution with G(t)

Established a relation for the dark energy equation of state at low redshift including G(t) corrections

Analyzed the impact of a time-dependent gravitational constant on dark energy behavior

Abstract

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.