Comparative Analysis of Holographic Dark Energy Models in $f(R,T^2)$ Gravity

This study investigates the Renyi Holographic dark energy, Sharma-Mittal Holographic dark energy and Generalized Holographic dark energy models in the framework of $f(R,T^2)$ gravity, where $R$ denotes the Ricci scalar and $T^2$ represents the self-contraction of the stress-energy tensor. For this purpose we employed two horizons as infrared cut-offs, such as Hubble horizon and Ricci horizon. The analysis is conducted for a non-interacting scenario in a spatially flat Friedmann-Robertson-Walker universe. By considering a specific form of this modified gravity, we reconstruct the corresponding gravitational models based on these selected dark energy formulations. Additionally, a stability analysis is performed for all cases and the evolution of the equation of state parameter is examined. Our finding indicates that the reconstructed $f(R,T^2)$ models effectively describe both the phantom and quintessence phases of cosmic evolution, aligning with the observed accelerated expansion of the universe. This study highlights the deep interconnections between holographic dark energy models and modified gravity theories, offering valuable insights into the large scale dynamics of the cosmos.