New tsallis holographic dark energy model and scalar fields for the bianchi type VIo universe model

In this thesis, the New Tsallis Holographic Dark Energy (NTHDE) model, proposed to explain the accelerated expansion of the universe, is examined within the framework of an anisotropic Bianchi Type VI₀ cosmological geometry. The study first presents in detail the theoretical foundations of the dark energy problem, the holographic principle, and dark energy models based on Tsallis entropy; subsequently, the mathematical structure of the NTHDE model is formulated. The Einstein field equations are derived for the anisotropic spacetime geometry, and the NTHDE energy density together with the equation-of-state parameter are calculated within this framework. The main approach of the thesis is based on reconstructing the NTHDE model through scalar field theories. In this context, three different scalar field models—tachyon, quintessence, and k-essence—are considered, and for each model the energy density, kinetic terms, and potential functions are established in correspondence with the NTHDE framework. The analyses are carried out under both exponential expansion and power-law expansion scenarios. For each expansion scheme, the time evolution of the equation-of-state parameter is investigated, and the resulting behaviors are compared for different model parameters. Using the derived equations, the kinetic and potential energy terms of the scalar fields are explicitly obtained, and their time evolution is illustrated through graphical representations. The analyses indicate that the NTHDE model exhibits a dynamical behavior spanning the cosmological constant limit, the quintessence regime, and the phantom regime, depending on the choice of model parameters. In the anisotropic Bianchi Type VI₀ universe, directional anisotropies are prominent in the early evolutionary stages, while at later times the model exhibits a more isotropic behavior.