Unveiling the Universe: Tsallis Holographic Dark Energy and Modified Logarithmic f(R) Gravity

In this paper, we delve into the intricacies of the Tsallis holographic dark energy model within the framework of a modified logarithmic f(R) gravity. This gravity model is distinctive due to its composition, which includes both polynomial terms and a logarithmic component. Our primary objective is to compute the equation of state parameter for the proposed model, which is a crucial step in understanding the behavior of dark energy in the universe. To achieve a comprehensive analysis, we employ two distinct scale factor structures: the exponential and the hybrid. The exponential scale factor is known for its simplicity and relevance in cosmological models that exhibit a constant rate of expansion. On the other hand, the hybrid scale factor offers a more nuanced approach, accommodating both early-time deceleration and late-time acceleration phases of the universe’s expansion. Furthermore, we rigorously test the stability of our model. One of the key methods we use is examining the sound speed, which serves as an indicator of the propagation of perturbations through the dark energy field. By plotting various figures, we can visually represent the stability conditions and analyze the viability of the Tsallis holographic dark energy model in a modified gravity context. Lastly, we meticulously document our findings, providing detailed expressions and calculations