Research Article Tsallis Holographic Dark Energy with Granda-Oliveros Scale in (+1)-Dimensional FRW Universe Ayman A. Aly Physics Department, Faculty of Science, Damanhour University, Damanhour, Egypt Correspondence should be addressed to Ayman A. Aly; ayman.aly@cern.ch Received 22 October 2018; Accepted 27 December 2018; Published 10 January 2019 Guest Editor: Pedro H. R. S. Moraes Copyright © 2019 Ayman A. Aly. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Based on Tsallis holographic dark energy model recently proposed by using the general model of the Tsallis entropy expression, we reconstruct cosmographic parameters, ,,,, and we study their evolution in spatially fat (+1)-dimensional Friedmann- Robertson-Walker universe using Granda-Oliveros scale. Our results show that the universe is in an accelerating expansion mode described by phantom-like behavior. We go further and study the state fnder operators and the  diagnostic to understand the behavior of our model. Te stability of the system is also studied by using the square of speed of sound showing that our model is stable over the low range of red-shif considered. Te results indicate that the entropy formalism will play an important role in understanding the dynamics of our universe. 1. Introduction Te study of accelerated expansion of the universe becomes one of the main hot topics in cosmology in the last few years [1–3]. Many theories are considered to explain this behavior. Actually, scientists believe that this accelerating behavior is mainly due to some repulsive gravity at large scale which is caused by a nonstandard component with negative pressure representing around two-thirds of universe known as dark energy . Tis accelerating behavior is characterized by equation of state (EoS) parameter which lies in a narrow region around the value EoS = -1. Te region corresponding to EoS parameter < -1 belongs to what is known as phantom dark energy (PDE) with an energy having positive energy density, but negative pressure. Te PDE is theoretically proposed by some models like braneworlds models or scalar-tensor gravity model [4–11]. Recent observations by Planck 2015, Baryon Acoustic Oscillations (BAO), Supernova Type Ia (SNIa), Large Scale Galaxy Surveys (LSS), and Weak Lensing (WL), show that Λ is the best candidate to explain the present acceler- ation of the universe [1–3, 12]. An interesting work by M. Li [13] assumed a new dark energy model called holographic dark energy model (HDE) based on what is called holographic principle. In this model the future event horizon of the universe can be used as infrared cutof. Actually, Tis model gives a good explanation for accelerated expansion nature of the universe and that fts the current observations. Tsallis and Cirto assumed some quantum modifcation for HDE by assuming that the black hole horizon entropy could be given by [14]   =   , (1) where  is an unknown constant and  denotes the nonaddi- tivity parameter chosen to have a positive value. By choosing =1 and  = 1/4 the Bekenstein entropy is easily recovered [14]. Te holographic principle, which states that the number of degrees of freedom of a physical system should be scaled with its bounding area rather than with its volume [13], should be constrained by an infrared cutof. Cohen et al. [15] proposed a relation between the system entropy  and the IR  and UV (Λ) cutofs as [16]  3 Λ 3 ≤ 3/4 . (2) Afer combining (1) with (3), one fnds Λ 4 ≤  (4)   2−4 , (3) Hindawi Advances in Astronomy Volume 2019, Article ID 8138067, 7 pages https://doi.org/10.1155/2019/8138067