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Tsallis entropy is a generalization of the Boltzmann–Gibbs entropy in statistical theory which uses a parameter δ 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 δ 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 , quintom behaviour for c < 1 whereas the Λ CDM model is recovered for c = 1 . To analyze the thermal history of the universe, we obtained the expression for the deceleration parameter and found that for z ≈ 0.6 , the phase transits from deceleration to acceleration. [ABSTRACT FROM AUTHOR]

In this manuscript, we present a novel dark energy scenario based on Kaniadakis entropy, which is a generalization of Boltzmann–Gibbs entropy that arises from relativistic statistical theory and is characterized by a parameter K which quantifies the deviations from standard expressions, and we use the age of the Universe as infrared cutoff. The cosmological characteristics of the proposed dark energy model, as well as the evolution of the cosmos filled with pressure-free matter and the ensuing dark energy candidates, are investigated. The interaction as well as non-interaction among the two sectors will also be considered. The differential equation for the dark energy density parameter, including the expression of the equation of state and deceleration parameters, are derived. The analysis of deceleration parameter clearly shows the universe to transit from decelerated to accelerated phase around z ≈ 0. 6. The most recent 30 H(z) data samples and the 580 Union 2.1 SNIa data set were also used to limit the theoretical results. The squared sound speed is also plotted against redshift z to check the stability behavior of the model for both the cases. • A novel dark energy model to study the cosmic acceleration. • Non-extensive Kaniadakis entropy. • Timescale as infrared cutoff. • The interaction as well as non-interaction among the two sectors have been considered. [ABSTRACT FROM AUTHOR]