Narrow Results

The statefinder parameters were introduced recently to differentiate different dark energy models. In this paper we perform a statefinder diagnostic to the phantom dark energy model with two different phantom field potentials. Our results show that the statefinder diagnostic is rather robust in differentiating not only different dark energy models but also the same kind of models with different potentials which lead to different fate of the universe.

In this paper, we investigate the role played by dark energy (DE) in the form of Generalized cosmic Chaplygin gas in an accelerating universe described by FRW cosmology. We have tried to describe the model from the theoretical point of view of a field, by introducing a scalar field ϕ and a self-interacting potential V(ϕ). The corresponding expressions for the field are obtained for the given model. Statefinder parameters have been used to characterize the dark energy model. Plots have been generated for characterizing different phases of universe diagrammatically and a comparative study is performed with the Modified Chaplygin gas model. As an outcome of the study, Generalized cosmic Chaplygin gas is identified as a much less constrained form of dark energy as compared to modified Chaplygin gas.

A useful method, known as statefinder diagnostic, which may differentiate one dark energy (DE) model from others is applied in this work to a holographic dark energy (HDE) model from Tsallis entropy, called the Tsallis holographic dark energy (THDE) model. The evolutionary trajectories of this model are plotted in the statefinder parameter — planes and $\omega -{\omega }^{\prime }$ plane, and it is observed that the parameter $\delta$ of this model plays a magnificent role from the statefinder and $\omega -{\omega }^{\prime }$ plane viewpoints. Eventually, the evolutionary trajectories are plotted considering two different values of THDE energy density (${\mathrm{\Omega }}_T^0$), ${\mathrm{\Omega }}_T^0=0.69$, in the light of Planck 2018 results VI base-LCDM cosmology and ${\mathrm{\Omega }}_T^0=0.73$, in the light of SNe + BAO + OHD + CMB observation data.

In this work, we have considered the recently proposed new Tsallis agegraphic dark energy (NTADE) model [Mod. Phys. Lett. A34, 1950086 (2019)] within the framework of a flat Friedmann–Robertson–Walker (FRW) Universe by taking various values of the parameter $\delta$. The NTADE model shows the current phase transition of the Universe from decelerated to accelerated phase. The NTADE equation of state (EoS) parameter shows a rich behavior as it can be quintessence-like or phantom-like depending on the value of $\delta$. For discriminating the NTADE model from $\mathrm{\Lambda }$CDM, we have plotted the statefinder parameters $r(z)$, $s(z)$ and $(r,s)$, $(r,q)$ pair. The NTADE model shows distinct evolutionary trajectories of their evolution in ($r,s$) and ($r,q$) plane. An analysis using the snap parameter and the ${\omega }_D-{\omega }_D^{\prime }$ pair dynamical analysis have also been performed.

New agegraphic dark energy (NADE) model with bulk viscosity is proposed by assuming that the universe is composed of the NADE and dark matter, and both the dark components have a bulk viscosity. At the matter-dominated epoch, the density parameter and the equation of state (EoS) of the viscous NADE are given by ${\mathrm{\Omega }}_q={(1-9{\tau }_m)}^2{n}^2{(1+z)}^{-2}∕4$ and $w_q=-2∕3+3({\tau }_q-{\tau }_m)$, respectively, where ${\tau }_q$ and ${\tau }_m$ are viscosity parameters. In the late time $z\to -1$, the NADE dominates ${\mathrm{\Omega }}_q\to 1$ and $w_q\to -1+3{\tau }_q$. Owing to the special analytic features at the matter-dominated epoch for the viscous NADE model, the initial condition ${\mathrm{\Omega }}_q(z_{\mathrm{\text{ini}}})={(1-9{\tau }_m)}^2{n}^2{(1+z_{\mathrm{\text{ini}}})}^{-2}∕4$ at $z_{\mathrm{\text{ini}}}=2000$ is used to solve the differential equation of ${\mathrm{\Omega }}_q$, and the other physical quantities can be obtained correspondingly. We also find that the viscosity of dark matter affects the current density and the start time of the cosmic acceleration. However, in the late time $w_q$ only depends on the viscosity of the dark energy. Furthermore, we investigate the viscous NADE model by means of statefinder diagnostic. The viscosity of dark matter significantly affects the evolution of the statefinder parameters. Therefore, the bulk viscosity plays a significant role in the cosmological evolution.

A new class of dark energy model, known as “Tsallis agegraphic dark energy (TADE),” has been proposed using the holographic principle and Tsallis nonextensive entropy (Mod. Phys. Lett. A, 2019), considering the conformal time as well as the age of the Universe as IR cutoffs in flat Universe. The trajectories for evolution of statefinder parameters in $(r,s)$, $(r,q)$, $(s,q)$ and the $({\omega }_D,{\omega }_D^{\prime })$ planes are plotted for the TADE 1 and TADE 2 models for the value of the Tsallis parameter $\delta$, and taking the TADE energy density parameter ${\mathrm{\Omega }}_D^0=0.70$, according to the Planck 2018 results VI — $\mathrm{\Lambda }$CDM observational data without interaction.

In this research, we examine a spatially homogeneous anisotropic locally rotationally symmetric (LRS) Bianchi type-I cosmological model in $f(R,T)$ gravity, for some choices of the function $f(R,T)=f_1(R)+f_2(T)$ (arXiv:1104.2669 [gr-qc]). The precise solutions of the field equations are introduced for the periodic-time varying deceleration parameter that can adjust to meet the $\mathrm{\Lambda }$CDM model. We have reviewed the physical and dynamic characteristics of these models to understand the accelerated expansion of the Universe in the current era. Furthermore, SNe Ia union data (arXiv:0811.2379 [astro-ph]), SN Ia with BAO and CMB observations (arXiv:1203.3213 [astro-ph.CO]) and OHD$+$JLA data (arXiv:1711.03437 [astro-ph.CO]) are used to estimate the statefinder diagnostics to get the geometric dynamics of the Universe at distinct stages and also to find the luminosity distance, angular-diameter distance, and distance modulus. We have also investigated the transit points for the deceleration parameter (q) in the framework of these three observations within the range of redshift $1.20\le z\le 1.65$.

We study the statefinder parameters in the Yang–Mills condensate dark energy models, and find that the evolving trajectories of these models are different from those of other dark energy models. We also define two eigenfunctions of the Yang–Mills condensate dark energy models. The values of these eigenfunctions are quite close to zero if the equation of state of the Yang–Mills condensate is not far from -1, which can be used to simply differentiate between the Yang–Mills condensate models and other dark energy models.

The quantum effective Yang–Mills condensate (YMC) dark energy model has some distinctive features so that it naturally solves the coincidence problem and, at the same time, is able to give an equation of state w crossing -1. In this work we further employ the statefinder pair (r,s), introduced by Sahni et al., to diagnose the YMC model for three cases: the noncoupling, the YMC decaying into matter only, and the YMC decaying into both matter and radiation. The trajectories (r,s) and (r,q), and the evolutions r(z) and s(z), are explicitly presented. It is found that the YMC model in all three cases has r ≃ 1 for z < 10 and s ≃ 0 for z < 5 with only small deviations, ≃ 0.02, quite close to the cosmological constant model (LCDM), but is obviously differentiated from other dark energy models, such as quiessence or kinessence.

This paper investigates the Tsallis holographic dark energy (THDE) model in accordance with the apparent horizon as an infrared cut-off, in a non flat universe. The cosmological evolution of the deceleration parameter and equation of state of THDE model are calculated. The evolutionary trajectories are plotted for the THDE model for distinct values of the Tsallis parameter $\delta$ besides distinct spatial curvature contributions, in the statefinder $(r,s)$ parameter-pairs and ${\omega }_D\text{–}{\omega }_D^{\prime }$ plane, considering the present value of dark energy (DE) density parameter ${\mathrm{\Omega }}_{D0}$, ${\mathrm{\Omega }}_{D0}=0.72$, in the light of $\mathrm{\text{WMAP}}+e\mathrm{\text{CMB}}+\mathrm{\text{BAO}}+H_0$ observational data. The statefinder and ${\omega }_D\text{–}{\omega }_D^{\prime }$ plane plots specify the feature of the THDE and demonstrate the separation between this framework and other models of DE.

This paper explores the interacting Tsallis holographic dark energy (THDE) model in a non-flat universe following an infrared cutoff as the apparent horizon. The equation of state (EoS) and the deceleration parameter of THDE model are determined to understand the cosmological evolution for interacting THDE model in the non-flat universe. By applying the statefinder $(r,s)$ parameter-pairs diagnostic and ${\omega }_D-{\omega }_D^{\prime }$ pair dynamical analysis for the derived THDE model, we plot the evolutionary trajectories for different cases of Tsallis parameter $\delta$ and interaction term $b^2$ and also, for spatial curvature ${\mathrm{\Omega }}_{k0}=0$, $-0.0012$ and $0.0026$ corresponding to flat, open and closed universes, respectively, in the framework of Planck 2018 base cosmology results VI-LCDM observational data.

In this study, the Kaniadakis holographic dark energy (KHDE) model is investigated within the framework of a flat FLRW universe by using an infrared cut-off as Hubble horizon. For the different values of the Kaniadakis parameter $\kappa$ and $C^2$, we perform an analysis on the deceleration, the equation of state and the energy density parameters. The current phase shift of the Cosmos may be rationalized by the change in sign of the deceleration parameter in the KHDE model, which went from $+ve$ to $-ve$, signifying a move from a phase of deceleration to one of acceleration. In order to get an understanding of the geometrical behavior shown by the KHDE model, we compute and show the statefinder evolutionary trajectory for the pairs $(r,s)$ and $(q,r)$. The evolutionary trajectory of ${\omega }_D-{\omega }_D^{\prime }$ reveals that the ${\omega }_D$ crosses the phantom divide line ${\omega }_D=-1$ at a late period in the evolutionary process. It has also been determined, by examination of the KHDE models stability analysis, that the model has behaved in an unstable manner during the whole course of the history of the universe. In addition to this, we optimized the model parameters by making use of the distance modulus measurement that was taken from the most current Union 2.1 dataset of supernovae.

Here, by employing a Barrow entropy and the standard holographic method at a cosmic framework, we formulate Barrow agegraphic dark energy (BADE), taking the Universe age as an IR cutoff scale in a flat FLRW Universe. For evaluation of statefinder parameters in $(r,s)$ and $(r,q)$ planes, trajectories have been plotted for BADE and discovered that for various values of $\mathrm{\Delta }$, the model exhibits both the behavior of Chaplygin gas and quintessence. Moreover, as a supplement to the statefinder study, we looked at the BADE model without interaction in the plane $({\omega }_D,{\omega }_D^{\prime })$, which might offer us a dynamic study using the energy density BADE parameter ${\mathrm{\Omega }}_D^0=0.70$ and $H_0=67$, as per VI-$\mathrm{\Lambda }$CDM observational data without interaction from Planck 2018 results.