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K. Karami
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Authors of ref. [1], M.R. Setare and S. Shafei (JCAP 09 (2006) 011), studied the thermodynamics of a holographic dark energy model in a non-flat universe enclosed by the apparent horizon $R_A$ and the event horizon measured from the sphere of the horizon named $L$. In section 3 in ref. [1], Authors showed that for $R_A$ the generalized second law of thermodynamics is respected, while for $L$ it is satisfied for the special range of the deceleration parameter. Here we present that their calculations for $R_A$ should be revised. Also we show that their conclusion for $L$ is not true and the generalized second law is hold for the present time independently of the deceleration parameter. Also if we take into account the contribution of dark matter in the generalized second law which is absent in ref. [1], then the generalized second law for $L$ is violated for the present time.
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In present research, we construct Kaniadakis holographic dark energy (KHDE) model within a non-flat Universe by considering the Friedmann-Robertson-Walker (FRW) metric with open and closed spatial geometries. We therefore investigate cosmic evolution by employing the density parameter of the dark energy (DE), the equation of state (EoS) parameter and the deceleration parameter (DP). The transition from decelerated to accelerated expanding phase for the KHDE Universe is explained through dynamical behavior of DP. With the classification of matter and DE dominated epochs, we find that the Universe thermal history can be defined through the KHDE scenario, and moreover, a phantom regime is experienceable. The model parameters are constrained by applying the newest $30$ data cases of $H(z)$ measurements, over the redshift span $0.07 leq z leq 2.36$, and the distance modulus measurement of the recent Union $2.1$ data set of type Ia supernovae. The classical stability of KHDE model has also been addressed.
Here we consider the entropy-corrected version of the new agegraphic dark energy model in the non-flat FRW universe. We derive the exact differential equation that determines the evolution of the entropy-corrected new agegraphic dark energy density parameter in the presence of interaction with dark matter. We also obtain the equation of state and deceleration parameters and present a necessary condition for the selected model to cross the phantom divide. Moreover, we reconstruct the potential and the dynamics of the phantom scalar field according to the evolutionary behavior of the interacting entropy-corrected new agegraphic model.
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In this paper, we have examined the R$acute{e}$nyi holographic dark energy (RHDE) model in the framework of an isotropic and spatially homogeneous flat FLRW (Friedmann- Lema$hat i$tre-Robertson-Walker) Universe by considering different values of parameter $delta$, where the infrared cut-off is taken care by the Hubble horizon. We examined the RHDE model through the analysis of the growth rate of perturbations and the statefinder hierarchy. The evolutionary trajectories of the statefinder hierarchy $S_3^1$, $S_3^2$ $S_4^1$, $S_4^2$ versus redshift $z$, shows satisfactory behaviour throughout the Universe evolution. One of the favourable appliance for exploring the dark energy models is the CND (composite null diagnostic) ${ S_3^1 - epsilon}$ and ${ S_4^1 - epsilon}$, where the evolutionary trajectories of the ${ S_3^1 - epsilon}$ and ${ S_4^1 - epsilon}$ pair show remarkable characteristics and the departure from $Lambda$CDM could be very much assessed.
Motivated by the work of Granda and Oliveros [L.N. Granda, A. Oliveros, Phys. Lett. B {bf 671}, 199 (2009)], we generalize their work to the non-flat case. We study the correspondence between the quintessence, tachyon, K-essence and dilaton scalar field models with the new holographic dark energy model in the non-flat FRW universe. We reconstruct the potentials and the dynamics for these scalar field models, which describe accelerated expansion of the universe. In the limiting case of a flat universe, i.e. $k = 0$, all results given in [L.N. Granda, A. Oliveros, Phys. Lett. B {bf 671}, 199 (2009)] are obtained.
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