Statefinder Hierarchy Research Articles

Diagnostic approaches for interacting generalized holographic Ricci dark energy models

In this paper, we present an analytical solution for the interacting generalized holographic dark energy model, assuming a linear interaction rate between dark energy and dark matter. We determine the equation of state parameter, the generalized holographic Ricci dark energy density, the matter density, and the deceleration parameter. By analyzing the behavior of these cosmological parameters, we demonstrate that our model aligns with recent observations and reproduces the late-time accelerated expansion of the Universe. To compare our model with the ΛCDM model, we use various diagnostic tools including statefinder, Om(z)-diagnostic, statefinder hierarchy, growth rate analysis, and ωH-ωH′ plane. We also analyze the stability of the model by examining the speed of sound. These methods show that the dynamics of the Universe remain very close to that of the standard cosmological model.

Theoretical analysis on the Barrow holographic dark energy in the DGP braneworld

This paper further studies the cosmological evolution and geometry diagnosis of Barrow holographic dark energy (BHDE) in the DGP braneworld, specifically, by choosing the interaction between dark energy and dark matter item. [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are discussed in the case of no interaction and four different interactions, the evolution laws of energy density parameters, deceleration parameters and EOS (equation of state) parameters of Barrow holographic dark energy. The results show that the Barrow holographic dark energy in the DGP braneworld conforms to the current cosmic evolution rule, already achieved the universe main ingredients from matter to the transition of energy, and explains the problem of cosmic acceleration. Further, in order to distinguish between the model and [Formula: see text]CDM model, this paper also geometrically diagnoses the model with the two ways of Statefinder hierarchy and Om[Formula: see text]. From their respective evolution image you can see, these two kinds of diagnosis methods can not only distinguish different from [Formula: see text]CDM model, but also can intuitively reflect the coupling parameters that can significantly affect the dark energy model.

Statefinder hierarchy of Kaniadakis holographic dark energy with composite null diagnostic

We investigate Kaniadakis holographic dark energy (KHDE) model taking the apparent horizon as the IR cutoff in a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. We apply variant dark energy (DE) diagnostic tool to study KHDE model in flat universe with different values of the constant [Formula: see text] and Kaniadakis entropy parameter [Formula: see text]. We use the tools statefinder hierarchy [Formula: see text], fractional growth parameter [Formula: see text] and composite null diagnostic (CND), which is blend of [Formula: see text] and [Formula: see text]. The evolution of trajectories of [Formula: see text] and [Formula: see text] depicts that there occur degeneracies in early time and also in the far future, whereas, in between these two extremes they are discriminated distinctly. The analysis of the present work shows that by the inclusion of fractional growth parameter [Formula: see text] with statefinder hierarchy (CND) degeneracy is removed reasonably, particularly more in the low redshift region.

Comparing entropy inspired holographic dark energy models through statefinder hierarchy and growth rate of perturbations

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 [Formula: see text] with the help of two diagnostic tools, in the context of a flat Friedmann–Lema[Formula: see text]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 [Formula: see text], [Formula: see text] [Formula: see text], [Formula: see text] has been investigated by plotting against redshift [Formula: see text]. The evolutionary trajectories of all the DE models approach the [Formula: see text]CDM model, except the TADE model for some values of [Formula: see text] at late time, are well discriminated with the [Formula: see text]CDM model at early time. To get more clear discrimination among the DE models at late time, we have used the CND, i.e. [Formula: see text][Formula: see text], where [Formula: see text] indicates the fractional growth parameter. The evolutionary trajectories of [Formula: see text] and [Formula: see text] show different characteristics and the departure from [Formula: see text]CDM could be well evaluated.

Statefinder hierarchy model for the Barrow holographic dark energy

In this paper, we have used the state finder hierarchy for Barrow holographic dark energy (BHDE) model in the system of the FLRW Universe. We apply two DE diagnostic tools to determine ΛBHDE model to have various estimations of ▵. The first diagnostic tool is the state finder hierarchy in which we have studied S3(1)S4(1), S3(2)S4(2) and second is the composite null diagnostic (CND) in which the trajectories (S3(1)−ϵ), (S4(1)−ϵ), (S3(2)−ϵ)(S4(2)−ϵ) are discussed, where ϵ is fractional growth parameter. The infrared cut-off here is taken from the Hubble horizon. Finally, together with the growth rate of matter perturbation, we plot the state finder hierarchy that determines a composite null diagnosis that can differentiate emerging dark energy from ΛCDM. In addition, the combination of the hierarchy of the state finder and the fractional growth parameter has been shown to be a useful tool for diagnosing BHDE, particularly for breaking the degeneracy with different parameter values of the model.

Dynamical Stability and Geometrical Diagnostic of the Power Law K-Essence Dark Energy Model with Interaction

We investigate the cosmological evolution of the power law k-essence dark energy (DE) model with interaction in FRWL spacetime with the Lagrangian that contains a kinetic function F(X)=−X+X. Concretely, the cosmological evolution in this model are discussed by the autonomous dynamical system and its critical points, together with the corresponding cosmological quantities, such as Ωϕ, wϕ, cs2, and q, are calculated at each critical point. The evolutionary trajectories are drawn in order to show the dynamical process on the phases plan around the critical points. The result that we obtained indicates that there are four dynamical attractors, and all of them correspond to an accelerating expansion of universe for certain potential parameter and coupling parameter. Besides that, the geometrical diagnostic by the statefinder hierarchy S3(1) and S4(1) of this scalar field model are numerically obtained by the phase components, as an extended null diagnostic for the cosmological constant. This diagnostic shows that both the potential parameter λ and interaction parameter α play important roles in the evolution of the statefinder hierarchy.

Exploring tsallis holographic dark energy scenario in [formula omitted] gravity

In this paper we have analysed Tsallis holographic dark energy in a flat Friedmann-Robertson-Walker model under the framework of f(R,T) gravity. The effects of this model in a non interactive universe are studied by taking different IR cut-offs that include particle horizon, event horizon, conformal age of the universe and GO (Granda-Oliveros) horizon. The cosmic evolution is studied by determining the conventional cosmological tools including the density parameter ΩDE, equation of state parameter ωDE and the deceleration parameter q. We have analysed the impact of these parameters by assuming different values for the matter-curvature coupling constant λ and the Tsallis parameter δ. We observe that all our four models exhibit appropriate behavior for the system parameters and support the accelerated expansion mode described by phantom-like scenario. Stability was only achieved for event horizon (partially) based on the speed of sound vs2. Furthermore we examined the behavior of our model by using various diagnostic mechanisms such as ωDE−ωDE′ analysis, statefinder pair (r,s),Om diagnostic and statefinder hierarchy S3(1) and S4(1). The trajectories of the ωDE−ωDE′ show a transition from freezing to thawing region, whereas r−s plane corresponds to a phase shift between Chaplygin gas model and quintessence model for particle and event horizon and solely Chaplygin gas model for conformal age and quintessence for GO-horizon. Om parameter also supports the quintessence era while statefinder hierarchy distinguishes our model effectively from the ΛCDM model and demonstrates the distinctive nature of all our models.

Diagnosing the Rényi holographic dark energy model in a flat Universe

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.

Exploring the Sharma–Mittal HDE models with different diagnostic tools

In this paper, we have examined the Sharma-Mittal holographic dark energy model (SMHDE) in the framework of an isotropic and spatially homogeneous flat Friedmann-Robertson-Walker(FRW) Universe by considering different values of parameter $\delta$ and $R$, where the infrared cut-off is taken care by the Hubble horizon. We examined the SMHDE model through the analysis of Statefinder hierarchy and the growth rate of perturbation. The evolutionary trajectories of the statefinder hierarchy $S_3^1$, $S_3^2$ $S_4^1$, $S_4^2$ versus redshift z, show satisfactory behavior throughout the Universe evaluation. One promising tool for investigating the dark energy models is the composite null diagnostic(CND) $\{ S_3^1 - \epsilon\}$, where the evolutionary trajectories of the $S_3^1 - \epsilon$ pair present different property and the departure from $\Lambda$CDM could be well evaluated. Additionally, we investigated the dynamical analysis of the model by $\omega_{D}-\omega^{'}_{D}$ pair analysis.

Statefinder hierarchy for Tsallis holographic dark energy

We apply the cosmological statefinder hierarchy to diagnose Tsallis holographic dark energy (THDE) models, which has been suggested by Tavayef et al. (2018), a new class of holographic dark energy (HDE) models in the non-flat universe. The IR cut off for the Tsallis holographic dark energy is taken as the apparent horizon. The evolutionary trajectories of statefinder hierarchy S31 and S41 against redshift z has been plotted. We observe from the evolutionary trajectories of S31 and S41, the statefinder hierarchy parameter S31 and S41 performs almost the same behavior and corresponds to the ΛCDM model in the future for all the three cases i.e flat, open and closed Universes.

Diagnosing Tsallis holographic dark energy models with interactions

It has been found that the geometrical diagnostic methods can break the degeneracy for dark energy models. In this paper, we investigate the Om diagnostic, the statefinder hierarchy [Formula: see text] and the composite null diagnostic [Formula: see text] for the Tsallis holographic dark energy models with interactions. We find that model parameters and the forms of interaction will influence the values of diagnostic parameters or the trends of the evolutionary trajectories for each model. Moreover, the statefinder hierarchy [Formula: see text] together with [Formula: see text] could give good diagnostic results. Furthermore, we also obtain some issues of cosmological structure by means of the composite null diagnostic.

Reconstructing the statefinder hierarchy for an interacting cosmology

This paper studies an interacting cosmology in a spatially flat universe. Here, we have reconstructed the interaction term, Q, between a cold dark matter (DM) fluid and a dark energy (DE) fluid, as well as a time-varying equation of state (EoS) parameter ωDE, and have explored its evolutionary trajectories in the second members of the statefinder hierarchy, allowing us to establish differences when they are compared with those obtained in other non-interacting models. Likewise, both Q and ωDE have been modeled in terms of the Chebyshev polynomials. Then, via a Markov chain Monte Carlo (MCMC) method, we have constrained the model parameter space by using a combined analysis of geometric data. Our results show that an interacting model can be distinguished well from the standard concordance model at the present time by using any combination of the second members of the statefinder hierarchy. In this way, different DE scenarios could be compared and distinguished between them.

A study of modified holographic Ricci dark energy in the framework of f(T) modified gravity and its statefinder hierarchy

Inspired by the work of Bamba et al. (Phys. Rev. D, 85, 104036 (2012)) the present paper reports a study on the reconstruction of modified holographic Ricci dark energy (MHRDE) in the framework of modified gravity taken as f(T) gravity. A correspondence between modified Chaplygin gas and MHRDE has also been considered and thereinafter the f(T) gravity has been reconstructed via reconstruction of the Hubble parameter. The reconstructed equation of state (EoS) parameter obtained this way has been found to be able to cross the phantom boundary. In the next phase of the work, a viable model of f(T) gravity has been considered and MHRDE has been discussed in this modified gravity frame. The EoS parameter due to the torsion contribution obtained this way has been found to behave like quintessence. The transition of the universe from the dark matter dominated to dark energy (DE) dominated phase is apparent from this model. Also, the model is exhibiting DE domination of the current universe. Finally, the statefinder hierarchy has been discussed through the statefinder and snap parameters. The model has been found to be able to attain the ΛCDM fixed point in the statefinder trajectory.

Constraining the dark energy statefinder hierarchy in a kinematic approach

In the present work, we have adopted a kinematic approach for constraining the extended null diagnostic of concordance cosmology, known as the statefinder hierarchy. A Taylor series expansion of the Hubble parameter has been utilised for the reconstruction. The coefficients of the Taylor series expansion are related to the kinematical parameters like the deceleration parameter, cosmological jerk parameter etc. The present values of the kinematical parameters are constrained from the estimated values of those series coefficients. A Markov chain Monte Carlo analysis has been carried out using the observational measurements of Hubble parameter at different redshifts, the distance modulus data of type Ia supernovae and baryon acoustic oscillation data to estimate the coefficient of series expansion of the Hubble parameter. The parameters in the statefinder diagnostic are related to the kinematical parameters. The statefinder diagnostic can form sets of hierarchy according to the order of the kinematical parameters. The present values of statefinder parameters have been constrained. The first set in the statefinder hierarchy allows ΛCDM to be well within the 1-σ confidence region, whereas the second set is in disagreement with the corresponding ΛCDM values at more than 1-σ level. Another dark energy diagnostic, namely the Om-parameters, is found to be consistent with concordance cosmology.

Some Interacting Dark Energy Models

In this paper, we study various cosmological models involving new nonlinear forms of interaction between cold dark matter (DM) and dark energy (DE) assuming that DE is a barotropic fluid. The interactions are nonlinear either due to log ( ρ d e / ρ d m ) or log ( ρ d m / ρ d e ) parameterizations, respectively. The main purpose of this paper is to demonstrate the applicability of the forms of suggested interactions to the problem of modern cosmology known as accelerated expansion of the Universe. Using the differential age of old galaxies expressed in terms of H ( z ) data, the peak position of baryonic acoustic oscillations (known as BAO data), the SN Ia data with strong gravitational lensing data, we obtain the best fit values of the model parameters for each case. Besides, using O m analysis and S 3 parameter from the statefinder hierarchy analysis, we also demonstrate that the considered models are clearly different from the Λ CDM model. We obtain that the models predict Hubble parameter values consistent to the estimations from gravitational lensing, which probes the expansion out to z ≤ 1.7 . We show that, with considered models, we can also explain PLANCK 2015 and PLANCK 2018 experiment results.

Diagnosing holographic type dark energy models with the Statefinder hierarchy, composite null diagnostic and w-w′ pair

The main purpose of this work is to distinguish various holographic type dark energy (DE) models, including the ΛHDE, HDE, NADE, and RDE model, by using various diagnostic tools. The first diagnostic tool is the Statefinder hierarchy, in which the evolution of Statefinder hierarchy parmeter S (1) 3(z) and S (1) 4(z) are studied. The second is composite null diagnostic (CND), in which the trajectories of {S (1) 3, ϵ} and {S (1) 4, ϵ} are investigated, where ϵ is the fractional growth parameter. The last is w-w′ analysis, where w is the equation of state for DE and the prime denotes derivative with respect to lna. In the analysis we consider two cases: varying current fractional DE density Ω de0 and varying DE model parameter C. We find that: (1) both the Statefinder hierarchy and the CND have qualitative impact on ΛHDE, but only have quantitative impact on HDE. (2) S (1) 4 can lead to larger differences than S (1) 3, while the CND pair has a stronger ability to distinguish different models than the Statefinder hierarchy. (3) For the case of varying C, the {w,w′} pair has qualitative impact on ΛHDE; for the case of varying Ω de0, the {w, w′} pair only has quantitative impact; these results are different from the cases of HDE, RDE, and NADE, in which the {w,w′} pair only has quantitative impact on these models. In conclusion, compared with HDE, RDE, and NADE, the ΛHDE model can be easily distinguished by using these diagnostic tools.

3-Form Cosmology: Phantom Behaviour, Singularities and Interactions

The latest cosmological observations by the Planck collaboration (and combined with others) are compatible with a phantom-like behaviour ( w < − 1 ) for the dark energy equation of state that drives the current acceleration of the Universe. With this mindset, we look into models where dark energy is described by a 3-form field minimally coupled to gravity. When compared to a scalar field, these models have the advantage of more naturally accommodating a cosmological-constant and phantom-like behaviours. We show how the latter happens for a fairly general class of positive-valued potentials, and through a dynamical system approach, we find that in such cases the 3-form field leads the Universe into a Little Sibling of the Big Rip singular event into the future. In this work, we explore the possibility of avoiding such singularity via an interaction in the dark sector between cold dark matter and the 3-form field. For the kind of interactions considered, we deduce a condition for replacing the LSBR by a late time de Sitter phase. For specific examples of interactions that meet this condition, we look for distinctive imprints in the statefinder hierarchy { S 3 ( 1 ) ; S 4 ( 1 ) } , { S 3 ( 1 ) ; S 5 ( 1 ) } , and in the growth rate of matter, ϵ ( z ) , through the composite null diagnostic (CND).

Cosmological implications of different baryon acoustic oscillation data

In this work, we explore the cosmological implications of different baryon acoustic oscillation (BAO) data, including the BAO data extracted by using the spherically averaged one-dimensional galaxy clustering (GC) statistics (hereafter BAO1) and the BAO data obtained by using the anisotropic two-dimensional GC statistics (hereafter BAO2). To make a comparison, we also take into account the case without BAO data (hereafter NO BAO). Firstly, making use of these BAO data, as well as the SNLS3 type Ia supernovae sample and the Planck distance priors data, we give the cosmological constraints of the $\Lambda$CDM, the $w$CDM, and the Chevallier-Polarski-Linder (CPL) model. Then, we discuss the impacts of different BAO data on cosmological consquences, including its effects on parameter space, equation of state (EoS), figure of merit (FoM), deceleration-acceleration transition redshift, Hubble parameter $H(z)$, deceleration parameter $q(z)$, statefinder hierarchy $S^{(1)}_3(z)$, $S^{(1)}_4(z)$ and cosmic age $t(z)$. We find that: (1) NO BAO data always give a smallest fractional matter density $\Omega_{m0}$, a largest fractional curvature density $\Omega_{k0}$ and a largest Hubble constant $h$; in contrast, BAO1 data always give a largest $\Omega_{m0}$, a smallest $\Omega_{k0}$ and a smallest $h$. (2) For the $w$CDM and the CPL model, NO BAO data always give a largest EoS $w$; in contrast, BAO2 data always give a smallest $w$. (3) Compared with the case of BAO1, BAO2 data always give a slightly larger FoM, and thus can give a cosmological constraint with a slightly better accuracy. (4) The impacts of different BAO data on the cosmic evolution and the comic age are very small, and can not be distinguished by using various dark energy diagnosis and the cosmic age data.

Interacting 3-form dark energy models: Distinguishing interactions and avoiding the Little Sibling of the Big Rip

In this paper we consider 3-form dark energy (DE) models with interactions in the dark sector. We aim to distinguish the phenomenological interactions that are defined through the dark matter (DM) and the DE energy densities. We do our analysis mainly in two stages. In the first stage, we identify the non-interacting 3-form DE model which generically leads to an abrupt late-time cosmological event which is known as the little sibling of the Big Rip (LSBR). We classify the interactions which can possibly avoid this late-time abrupt event. We also study the parameter space of the model that is consistent with the interaction between DM and DE energy densities at present as indicated by recent studies based on BAO and SDSS data. In the later stage, we observationally distinguish those interactions using the statefinder hierarchy parameters $\{ S_{3}^{(1)}\,,\, S_{4}^{(1)}\} \,,\,\{ S_{3}^{(1)}\,,\, S_{5}^{(1)}\} .$ We also compute the growth factor parameter $\epsilon(z)$ for the various interactions we consider herein and use the composite null diagnostic (CND) $\{ S_{3}^{(1)}\,,\,\epsilon(z)\} $ as a tool to characterise those interactions by measuring their departures from the concordance model. In addition, we make a preliminary analysis of our model in light of the recently released data by SDSS~III on the measurement of the linear growth rate of structure.

Impacts of different SNLS3 light-curve fitters on cosmological consequences of interacting dark energy models

We explore the cosmological consequences of interacting dark energy (IDE) models using the SNLS3 supernova samples. In particular, we focus on the impacts of different SNLS3 light-curve fitters (LCF) (corresponding to "SALT2", "SiFTO", and "Combined" sample). Firstly, making use of the three SNLS3 data sets, as well as the Planck distance priors data and the galaxy clustering data, we constrain the parameter spaces of three IDE models. Then, we study the cosmic evolutions of Hubble parameter $H(z)$, deceleration diagram $q(z)$, statefinder hierarchy $S^{(1)}_3(z)$ and $S^{(1)}_4(z)$, and check whether or not these dark energy diagnosis can distinguish the differences among the results of different SNLS3 LCF. At last, we perform high redshift cosmic age test using three old high redshift objects (OHRO), and explore the fate of the Universe. We find that, the impacts of different SNLS3 LCF are rather small, and can not be distinguished by using $H(z)$, $q(z)$, $S^{(1)}_3(z)$, $S^{(1)}_4(z)$, and the age data of OHRO. In addition, we infer, from the current observations, how far we are from a cosmic doomsday in the worst case, and find that the "Combined" sample always gives the largest 2$\sigma$ lower limit of the time interval between "big rip" and today, while the results given by the "SALT2" and the "SiFTO" sample are close to each other. These conclusions are insensitive to a specific form of dark sector interaction. Our method can be used to distinguish the differences among various cosmological observations.