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By extending the standard holographic principle to a cosmological framework and combining the non-flat condition with the Kaniadakis entropy, we construct the non-flat Kaniadakis holographic dark energy (KHDE) model. The model employs Kaniadakis parameter K and a parameter c. Derivation of the differential equation for KHDE density parameter to describe the evolutionary behavior of the universe is obtained. Such a differential equation could explain both the open as well as closed universe models. The classification based on matter and dark energy (DE) dominated regimes show that the KHDE scenario may be used to specify the universe’s thermal history and that a quintom regime can be encountered. For both open and closed, we find the expressions for the deceleration parameter and the equation of state (EoS) parameter. Also, by varying the associated parameters, classical stability of the method is established. On considering the curvature to be positive, the universe favors the quintom behavior for substantially smaller values as opposed to the flat condition, when only quintessence is attained for such K values. Additionally, we see a similar behavior while considering the negative curvature for such K values. Therefore, adding a little bit of spatial geometry that isn’t flat to the KHDE enhances the phenomenology while maintaining K values at lower levels. To validate the model parameters, the most recent 30 H (z) dataset, in the redshift range 0.07 ≤ z ≤ 1.965 are utilized. In addition, the distance modulus from the current Union 2.1 data set of type SNIa are employed. [ABSTRACT FROM AUTHOR]

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]