New Tsallis holographic dark energy
Bramha Dutta Pandey, P. Suresh Kumar, Pankaj, Umesh Kumar Sharma
Abstract
Abstract Tsallis entropy is a generalization of the Boltzmann–Gibbs entropy in statistical theory which uses a parameter $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> to measure the deviation from the standard scenario quantitatively. Using concepts of Tsallis entropy and future event horizon, we construct a new Tsallis holographic dark energy model. The parameters c and $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> will be used to characterize various aspects of the model. Analytical expressions for various cosmological parameters such as the differential equation describing the evolution of the effective dark energy density parameter, the equation of state parameter and the deceleration parameter are obtained. The equation of state parameter for the current model exhibits the pure quintessence behaviour for $$c>1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , quintom behaviour for $$c<1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> whereas the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model is recovered for $$c=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . To analyze the thermal history of the universe, we obtained the expression for the deceleration parameter and found that for $$z \approx 0.6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> </mml:math> , the phase transits from deceleration to acceleration.