Bianchi type-III THDE quintessence model with hybrid scale factor

The current research investigates the behavior of the Tsallis holographic dark energy (THDE) model with quintessence in a homogeneous and anisotropic Bianchi type-III (B-III) space-time. We construct the model by using two conditions (i) expansion scalar (\theta) is proportionate to shear scalar (\sigma) in the model and (ii) hybrid {\color{blue} scale factor} a = t^\beta e^{\gamma t}, where \beta>0, \gamma>0 are constants. Our study is based on Type Ia supernovae (SNIa) data in combination with CMB and BAO observations (Giostri et al, JCAP 3, 27 (2012), arXiv:1203.3213v2[astro-ph.CO]), the present values of Hubble constant and deceleration parameter are H_{0} = 73.8 and q_{0} = -0.54 respectively. Compiling our theoretical models with this data, we obtain \beta = 2.1445~ \& ~ 2.1154 for \gamma = 0.5 ~ \& ~ 1 respectively. We completed an entirely novel form of cosmic model where the expansion occurs during the present accelerated phase for the constraints. We have discussed the conformity among the scalar field model of quintessence and THDE model. To understand the Universe, we have also established the relations for Distance modulus, Luminosity distance, and Angular-diameter distance. Some geometric and physical aspects of the THDE model are also highlighted.