# Cosmic Evolution of Holographic Dark Energy in f(\mathcal{G},T) Gravity

## TL;DR

This paper explores the evolution of holographic dark energy within a modified gravity framework involving Gauss-Bonnet invariant and trace of energy-momentum tensor, revealing a phantom epoch and accelerated expansion.

## Contribution

It reconstructs a specific $f( ext{G},T)$ gravity model for holographic dark energy using a power-law scale factor and analyzes its cosmological implications.

## Key findings

- Universe exhibits phantom epoch behavior.
- Model indicates accelerated cosmic expansion.
- State-finder analysis aligns with Chaplygin gas characteristics.

## Abstract

The aim of this paper is to analyze the cosmological evolution of holographic dark energy in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively). We reconstruct $f(\mathcal{G},T)$ model through correspondence scheme using power-law form of the scale factor. The qualitative analysis of the derived model is investigated with the help of evolutionary trajectories of equation of state, deceleration as well as state-finder diagnostic parameters and $\omega_{_{\mathcal{G}T}}-{\omega}'_{_{\mathcal{G}T}}$ cosmological phase plane. It is found that the equation of state parameter represents phantom epoch of the Universe whereas the deceleration parameter illustrates the accelerated phase. The state-finder plane corresponds to Chaplygin gas model while the freezing region is attained in $\omega_{_{\mathcal{G}T}}-{\omega}'_{_{\mathcal{G}T}}$ plane.