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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 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 open and closed both the cases, 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 curvature to be negative 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 measurements, in the redshift range $0.07 \leq z \leq 1.965$ are utilized. In addition, the distance modulus measurement from the current Union 2.1 data set of type Ia supernovae are employed., Comment: 17 pages, 12 figures

The proposed model is a study of the nature of dark energy through non-extensive Tsallis entropy. The method is based on the Karolyhazy relation which is a combined idea from quantum physics and general relativity. Dark energy is the energy density of quantum fluctuations in space-time. This is the key idea behind proposing agegraphic dark energy (ADE) models here. The parameter $\delta$ is used to measure the quantitative distinction from the standard scenario. To look at the cosmological implications of the hypothesized dark energy model, as well as the expansion of the Universe filled with zero pressure matter and the resulting dark energy alternatives, the role of IR cutoff is played by age of the universe. The dynamic behavior of dark energy density parameter is carried out. The expressions for the equation of state parameter and deceleration parameter are obtained. The analysis is performed by taking into account a no flow as well as a flow of energy among the dark matter and dark energy sectors of the universe., Comment: 10 pages, 20 figures

In this manuscript, we present a novel dark energy model to study the nature of dark energy. Non-extensive Kaniadakis entropy and, timescale as infrared cutoff are the major tools of the current study. Age of the Universe will serve the purpose of 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 $z\approx 0.6$. The squared sound speed is also plotted against redshift $z$ to check the stability behavior of the model for both the cases., Comment: 17 pages, 20 figures

Tsallis entropy is a generalization of the Boltzmann-Gibbs entropy in statistical theory which uses a parameter $\delta$ 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 $\delta$ 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 $\Lambda$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 $z \approx 0.6$, the phase transits from deceleration to acceleration., Comment: 14 pages, 7 figures