Correspondence between $f(G)$ Gravity and Holographic Dark Energy via Power-law Solution

TL;DR

This paper explores the connection between $f(G)$ modified gravity and holographic dark energy using a power-law cosmological model, revealing a quintessence-like behavior but also indicating instability in the model.

Contribution

It constructs a specific $f(G)$ gravity model incorporating holographic dark energy and analyzes its cosmological behavior with a power-law scale factor.

Findings

The reconstructed $f(G)$ model satisfies conditions for realistic modified gravity.

The effective EoS parameter indicates quintessence behavior.

The model exhibits instability due to negative squared sound speed.

Abstract

In this paper, we discuss cosmological application of holographic Dark Energy (HDE) in the framework of $f(G)$ modified gravity. For this purpose, we construct $f(G)$ model with the inclusion of HDE and a well-known power law form of the scale factor $a(t)$. The reconstructed $f(G)$ is found to satisfy a sufficient condition for a realistic modified gravity model. We find quintessence behavior of effective equation of state (EoS) parameter $\omega_{DE}$ through energy conditions in this context. Also, we observe that the squared speed of sound $v_s^2$ remains negative which shows the instability of HDE $f(G)$ model.