Bianchi type-III Tsallis holographic dark energy model in Saez–Ballester theory of gravitation
M. Vijaya Santhi, Y. Sobhanbabu
Abstract
Abstract In this paper, we have investigated Tsallis holographic dark energy (infrared cutoff is the Hubble radius) in homogeneous and anisotropic Bianchi type- III Universe within the framework of Saez–Ballester scalar–tensor theory of gravitation. We have constructed non-interaction and interaction dark energy models by solving the Saez–Ballester field equations. To solve the field equations, we assume a relationship between the metric potentials of the model. We developed the various cosmological parameters (namely deceleration parameter q , equation of state parameter $$\omega _t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> , squared sound speed $$v_s^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> , om-diagnostic parameter Om ( z ) and scalar field $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> ) and well-known cosmological planes (namely $$\omega _t-\omega _t^{'}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msubsup> <mml:mi>ω</mml:mi> <mml:mi>t</mml:mi> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:msubsup> </mml:mrow> </mml:math> plane, where $$'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:math> denotes derivative with respect to ln ( a ) and statefinders ( $$r-s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> ) plane) and analyzed their behavior through graphical representation for our both the models. It is also, quite interesting to mention here that the obtained results are coincide with the modern observational data.