Narrow Results

In this paper, we construct a holographic dark energy (HDE) model considering the IR cut-off as Hubble horizon, holographic hypothesis, and using the generalized Rényi entropy, and investigate its cosmological outcomes in Brans–Dicke gravity without interaction. We observe the suitable behavior for the cosmological parameters, involving the deceleration parameter, the equation of state (EoS) parameter, and the density parameter in both flat and non-flat Universes. It is also concluded by the stability analysis that the Rényi holographic dark energy (RHDE) model is classically stable at present and future for the Rényi parameter $\delta$ in both flat and non-flat Universe.

In this work, we study the cosmological consequences of Rényi holographic dark energy model in the framework of the Finsler–Randers cosmology in which the Hubble horizon is considered as the IR cutoff. In this setup, we derive the evolution equation for the Rényi holographic dark energy density parameter, the equation of state (EoS) parameter and deceleration parameter. Our study shows that this model can describe the current accelerating universe in both noninteracting and interacting scenarios, and also a transition occurs from the deceleration phase to the accelerated phase at the late-time. Moreover, we discuss the statefinder diagnosis of this model, meanwhile, plot the curves of r and s versus redshift z and the evolutionary trajectories of $\{r,s\}$. We find that statefinder can not only break the degeneracy of different coupling parameter values in this model, but also effectively distinguish the difference between the Rényi holographic dark energy model and the $\mathrm{\Lambda }$CDM model. In addition, we find that the statefinder pair $\{r,s\}$ performs better than $\{r,z\}$ and $\{s,z\}$ in this model.

In this paper, we have investigated some recently proposed entropy-based versions of various HDE models, namely, the TADE, THDE, RHDE and SMHDE for different values of model parameter $\delta$ with the help of two diagnostic tools, in the context of a flat Friedmann–Lema$î$tre–Robertson–Walker Universe. The statefinder hierarchy is the first diagnostic tool, by which we examine these DE models. The evolution of statefinder hierarchy parameters $S_3^1$, $S_3^2$$S_4^1$, $S_4^2$ has been investigated by plotting against redshift $z$. The evolutionary trajectories of all the DE models approach the $\mathrm{\Lambda }$CDM model, except the TADE model for some values of $\delta$ at late time, are well discriminated with the $\mathrm{\Lambda }$CDM model at early time. To get more clear discrimination among the DE models at late time, we have used the CND, i.e. $\{S_3^{(1)},𝜖\}$$\{S_4^{(1)},𝜖\}$, where $𝜖$ indicates the fractional growth parameter. The evolutionary trajectories of $\{S_3^{(1)},𝜖\}$ and $\{S_4^{(1)},𝜖\}$ show different characteristics and the departure from $\mathrm{\Lambda }$CDM could be well evaluated.

In this work, we study the Rényi holographic dark energy (RHDE) model in a flat FRW Universe where the infrared cut-off is taken care by the Hubble horizon and also by taking three different parametrizations of the interaction term between the dark matter and the dark energy. Analyzing graphically, the behavior of some cosmological parameters in particular deceleration parameter, equation of state (EoS) parameter, energy density parameter and squared speed of sound, in the process of the cosmic evolution, is found to be leading towards the late-time accelerated expansion of the RHDE model. Also, we find the departure for the derived models from the standard $\mathrm{\Lambda }$CDM model according to the evolution of jerk parameter. Moreover, we compare the model parameters by considering the observational Hubble data which consist of 51 points in the redshift range $0.07<z<2.36$.