Physics Maths Engineering
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In this paper we consider the correspondence between the tachyon dark energy model and the Tsallis holographic dark energy scenario in an FRW universe. We demonstrate the Tsallis holographic description of tachyon dark energy in an FRW universe and reconstruct the potential and basic results of the dynamics of the scalar field which describe the tachyon cosmology. In a flat universe, in the tachyon model of Tsallis holographic dark energy, independently of the existence of interaction between dark energy and matter or not, T˙ 2 must always be zero. Therefore, the equation of state ωD is always −1 in such a flat universe. For a non-flat universe, T˙ 2 cannot be zero so that ωD 6= −1 which cannot be used to explain the origin of the cosmological constant. T˙ 2 monotonically decreases with the increasing of cos(Rh/a) and cosh(Rh/a) for different δs. In particular, for an open universe, T˙ 2 is always larger than zero while for a closed universe, T˙ 2 is always smaller than zero which is physically invalid. In addition, we conclude that with the increasing of cos(Rh/a) and cosh(Rh/a), T˙ 2 always decreases monotonically for irrespective of the value of b2.