Holographic Dark Energy in Barrow Cosmology with Granda-Oliveros IR Cutoff

Applying the modified Barrow entropy, inspired by the quantumfluctuation effects, to the cosmological background, and usingthermodynamics-gravity conjuncture, the Friedmann equations getmodified as well. In this paper, we explore the holographic darkenergy with Granda-Oliveros (GO) IR cutoff, in the context of themodified Barrow cosmology. First, we assume two dark components ofthe universe evolves independently and obtain the cosmologicalparameters and explore the cosmic evolution. Second, we consideran interaction term between dark energy (DE) and dark matter (DM).We observe that the Barrow parameter $\delta$ crucially affectsthe cosmic dynamics, causes the transition from the deceleratingphase to the accelerating phase occurs later. We find out that theequation of state parameter is in the quintessence region in thepast and crosses the phantom divide at the present time. Finally,we examine the squared speed of sound analysis for this model.According to the squared sound speed diagrams, the resultsindicate that the presence of interaction between DM and DE  aswell as increasing in the value of $\delta$ leads to themanifestation of signs of instability in the past $(v_s^2<0)$.Furthermore, by examining the statefinder, we find that presenceof  $\delta$ also makes a distinction between holographic darkenergy in Barrow cosmology with GO-IR cutoff and the $\Lambda$CDMmodel. In fact, increasing $\delta$ causes the statefinder diagrammove away from the point of $\left\lbrace r,s\right\rbrace=\left\lbrace 1,0\right\rbrace$ at $z=0$.