Tsallis holographic dark energy model in an anisotropic universe with linearly varying deceleration parameter and its correspondence with phantom

In this paper, we investigate a spatially homogeneous and anisotropic Bianchi type-I universe filled with cold dark matter and Tsallis holographic dark energy within the framework of General Relativity. We assume the cold dark matter and the Tsallis holographic dark energy to be non-interacting and obtain exact solutions of the Einstein field equations by considering a linearly varying deceleration parameter. The physical and kinematical properties of the resulting model are explored through different parameters of cosmological importance such as the Hubble parameter, the anisotropy parameter, the equation of state parameter, the jerk parameter, the snap parameter, the lerk parameter etc. The validation or violation of the four energy conditions are also checked. We find that the Weak and Dominant Energy Conditions are fulfilled but the Null and Strong Energy Conditions are violated at late time which supports the accelerated expansion of the universe. In addition, we establish the correspondence between phantom scalar field model and Tsallis holographic dark energy model.