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Register a new userBarrow HDE model for Statefinder diagnostic in FLRW Universe
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We have analyzed the Barrow holographic dark energy (BHDE) in the framework of the flat FLRW Universe by considering the various estimations of Barrow exponent $triangle$. Here we define BHDE, by applying the usual holographic principle at a cosmological system, for utilizing the Barrow entropy rather than the standard Bekenstein-Hawking. To understand the recent accelerated expansion of the universe, considering the Hubble horizon as the IR cut-off. The cosmological parameters, especially the density parameter ($Omega_{_D}$), the equation of the state parameter ($omega_{_D}$), energy density ($rho_{_{D}}$) and the deceleration parameter($q$) are studied in this manuscript and found the satisfactory behaviors. Moreover, we additionally focus on the two geometric diagnostics, the statefinder $(r,s)$ and $O_{m}(z)$ to discriminant BHDE model from the $Lambda CDM$ model. Here we determined and plotted the trajectories of evolution for statefinder $(r, s)$, $(r,q)$ and $O_{m}(z)$ diagnostic plane to understand the geometrical behavior of the BHDE model by utilizing Planck 2018 observational information. Finally, we have explored the new Barrow exponent $triangle$, which strongly affects the dark energy equation of state that can lead it to lie in the quintessence regime, phantom regime, and exhibits the phantom-divide line during the cosmological evolution.
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In this work we study a non-flat Friedmann-Robertson-Walker universe filled with a pressure-less dark matter (DM) and Barrow holographic dark energy (BHDE) whose IR cutoff is the apparent horizon. Among various DE models, (BHDE) model shows the dynamical enthusiasm to discuss the universes transition phase. According to the new research, the universe transitioned smoothly from a decelerated to an accelerated period of expansion in the recent past. We exhibit that the development of $q$ relies upon the type of spatial curvature. Here we study the equation of state (EoS) parameter for the BHDE model to determine the cosmological evolution for the non-flat universe. The (EoS) parameter and the deceleration parameter (DP) shows a satisfactory behaviour, it does not cross the the phantom line. We also plot the statefinder diagram to characterize the properties of the BHDE model by taking distinct values of barrow exponent $triangle$. Moreover, we likewise noticed the BHDE model in the $(omega_{D}-omega_{D}^{})$ plane, which can furnish us with a valuable, powerful finding to the mathematical determination of the statefinder. In the statefinder trajectory, this model was found to be able to reach the $Lambda CDM$ fixed point.
We have developed an accelerating cosmological model for the present universe which is phantom for the period $ (0 leq z leq 1.99)$ and quintessence phase for $(1.99 leq z leq 2.0315)$. The universe is assumed to be filled with barotropic and dark energy(DE) perfect fluid in which DE interact with matter. For a deceleration parameter(DP) having decelerating-accelerating transition phase of universe, we assume hybrid expansion law for scale factor. The transition red shift for the model is obtained as $z_t = 0.956$. The model satisfies current observational constraints.
We focus on a series of $f(R)$ gravity theories in Palatini formalism to investigate the probabilities of producing the late-time acceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We apply statefinder diagnostic to these cosmological models for chosen series of parameters to see if they distinguish from one another. The diagnostic involves the statefinder pair ${r,s}$, where $r$ is derived from the scale factor $a$ and its higher derivatives with respect to the cosmic time $t$, and $s$ is expressed by $r$ and the deceleration parameter $q$. In conclusion, we find that although two types of $f(R)$ theories: (i) $f(R) = R + alpha R^m - beta R^{-n}$ and (ii) $f(R) = R + alpha ln R - beta$ can lead to late-time acceleration, their evolutionary trajectories in the $r-s$ and $r-q$ planes reveal different evolutionary properties, which certainly justify the merits of statefinder diagnostic. Additionally, we utilize the observational Hubble parameter data (OHD) to constrain these models of $f(R)$ gravity. As a result, except for $m=n=1/2$ of (i) case, $alpha=0$ of (i) case and (ii) case allow $Lambda$CDM model to exist in 1$sigma$ confidence region. After adopting statefinder diagnostic to the best-fit models, we find that all the best-fit models are capable of going through deceleration/acceleration transition stage with late-time acceleration epoch, and all these models turn to de-Sitter point (${r,s}={1,0}$) in the future. Also, the evolutionary differences between these models are distinct, especially in $r-s$ plane, which makes the statefinder diagnostic more reliable in discriminating cosmological models.
Using a new method--statefinder diagnostic which can differ one dark energy model from the others, we investigate in this letter the dynamics of Born-Infeld(B-I) type dark energy model. The evolutive trajectory of B-I type dark energy with Mexican hat potential model with respect to $e-folding$ time $N$ is shown in the $r(s)$ diagram. When the parameter of noncanonical kinetic energy term $etato0$ or kinetic energy $dot{phi}^2to0$, B-I type dark energy(K-essence) model reduces to Quintessence model or $Lambda$CDM model corresponding to the statefinder pair ${r, s}$=${1, 0}$ respectively. As a result, the the evolutive trajectory of our model in the $r(s)$ diagram in Mexican hat potential is quite different from those of other dark energy models.
Statefinder diagnostic is a useful method which can differ one dark energy model from the others. The Statefinder pair ${r, s}$ is algebraically related to the equation of state of dark energy and its first time derivative. We apply in this paper this method to the dilaton dark energy model based on Weyl-Scaled induced gravitational theory. We investigate the effect of the coupling between matter and dilaton when the potential of dilaton field is taken as the Mexican hat form. We find that the evolving trajectory of our model in the $r-s$ diagram is quite different from those of other dark energy models.
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