Barrow HDE model for Statefinder diagnostic in non-flat FRW universe

TL;DR

This paper investigates a non-flat universe with Barrow holographic dark energy, analyzing its evolution and diagnostic parameters, and finds it can reach the standard Lambda-CDM model in the statefinder plane.

Contribution

It introduces a detailed analysis of the BHDE model in a non-flat universe using statefinder diagnostics and explores its behavior relative to the Lambda-CDM model.

Findings

The universe transitions from decelerated to accelerated expansion.

The EoS parameter remains above the phantom line.

The model's statefinder trajectory reaches the Lambda-CDM fixed point.

Abstract

In this work we study a non-flat Friedmann-Robertson-Walker universe filled with a pressure-less dark matter (DM) and Barrow holographic dark energy (BHDE) whose IR cutoff is the apparent horizon. Among various DE models, (BHDE) model shows the dynamical enthusiasm to discuss the universe's transition phase. According to the new research, the universe transitioned smoothly from a decelerated to an accelerated period of expansion in the recent past. We exhibit that the development of $q$ relies upon the type of spatial curvature. Here we study the equation of state (EoS) parameter for the BHDE model to determine the cosmological evolution for the non-flat universe. The (EoS) parameter and the deceleration parameter (DP) shows a satisfactory behaviour, it does not cross the the phantom line. We also plot the statefinder diagram to characterize the properties of the BHDE model by taking distinct values of barrow exponent $\triangle$. Moreover, we likewise noticed the BHDE model in the $(\omega_{D}-\omega_{D}^{'})$ plane, which can furnish us with a valuable, powerful finding to the mathematical determination of the statefinder. In the statefinder trajectory, this model was found to be able to reach the $\Lambda CDM$ fixed point.