Comparative Analysis of Holographic Dark Energy Models in $f(R,T^2)$ Gravity
M. Sharif, M. Zeeshan Gul, I. Hashim
TL;DR
This work investigates three holographic dark energy models—Rényi HDE, Sharma-Mittal HDE, and Generalized HDE—in the $f(R,T^2)$ gravity framework with a flat FRW background. By adopting the explicit gravity form $f(R,T^2)=\alpha R^n+\beta T^2$ and exploring both the Hubble and Ricci IR cutoffs, the study reconstructs the corresponding DE sectors, analyzes their stability, and examines the evolution of the equation of state. The analysis demonstrates that the reconstructed models can describe both phantom and quintessence phases, offering a bridge between holographic DE concepts and modified gravity, and showing compatibility with low-redshift observations such as cosmic chronometer data. These results underscore the potential of holographic-DE constructs within energy-momentum squared gravity to account for late-time cosmic acceleration and illuminate the interplay between entropy-based DE models and geometry–matter couplings.
Abstract
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.