Barrow holographic dark energy: a path to reconstructing $f(R,T)$ gravity

In this paper, we investigate one of the established methods for reconstructing modified gravity models from a dark energy model, with the aim of discovering relationships between these theories. In this study, we focus on the $f(R,T)$ modified gravity theory, where $R$ denotes the Ricci scalar and $T$ represents the trace of the energy-momentum tensor. We employ Barrow's holographic dark energy model, derived from fractal surfaces of black holes, to investigate the reconstruction process. The numerical results are subsequently presented for various infrared cutoffs, such as the Hubble horizon, future event horizon, and Granda-Oliveros cutoff.