Narrow Results

In this research, we have reconstructed the extended $f({𝒫})$ cubic gravity and symmetric $f({𝒬})$ teleparallel gravity from the $(m,n)$-type Barrow Holographic Dark Energy (BHDE) model. We have derived the unknown functions $f({𝒫})$ and $f({𝒬})$ in terms of ${𝒫}$ and ${𝒬}$, assuming a flat, homogeneous, and isotropic universe. To constrain our model parameters, we employed cosmic chronometer datasets and Baryon Acoustic Oscillation (BAO) datasets, utilizing Markov Chain Monte Carlo (MCMC) method. We analyzed the behavior and stability of each model throughout the universe’s evolution by studying crucial parameters such as the deceleration parameter, equation of state (EoS) parameter ${\omega }_{\mathrm{\text{DE}}}$, density parameter $\mathrm{\Omega }(z)$ and the square of the speed of sound $v_s^2$. Additionally, we explored the cosmographic behavior by plotting the jerk parameter, snap parameter, and lerk parameter against the redshift. Furthermore, we examined the ${\omega }_{\mathrm{\text{DE}}}^{\prime }-{\omega }_{\mathrm{\text{DE}}}$ phase plane, the $(r,s^{\ast })$, $(r,q)$ statefinder parameters, and the $Om(z)$ parameter offers profound revelations about the dynamics of the universe and the distinctive features of dark energy. Our analyses indicated that our model could produce a universe undergoing accelerated expansion with quintessence-type dark energy. These findings contribute to our understanding of the nature of dark energy and the evolution of the cosmos.

Using the absolute ages of passively evolving galaxies observed at different redshifts, one can obtain the differential ages, the derivative of redshift z with respect to the cosmic time t (i.e. dz/dt). Thus, the Hubble parameter H(z) can be measured through the relation H(z) = -(dz/dt)/(1+z). By comparing the measured Hubble parameter at different redshifts with the theoretical one containing free cosmological parameters, one can constrain current cosmological models. In this paper, we use this method to present the constraint on a spatially flat Friedman–Robert–Walker universe with a matter component and a holographic dark energy component, in which the parameter c plays a significant role in this dark energy model. Firstly we consider three fixed values of c = 0.6, 1.0 and 1.4 in the fitting of data. If we set c free, the best fitting values are c = 0.26, Ω_m0 = 0.16, h = 0.9998. It is shown that the holographic dark energy behaves like a quintom-type at the 1σ level. This result is consistent with some other independent cosmological constrains, which imply that c < 1.0 is favored. We also test the results derived from the differential ages using another independent method based on the lookback time to galaxy clusters and the age of the universe. It shows that our results are reliable.

We investigate a model of brane cosmology to find a unified description of the radiation-matter-dark energy universe. It is of the interacting holographic dark energy with a bulk-holographic matter χ. This is a five-dimensional cold dark matter, which plays a role of radiation on the brane. Using the effective equations of state instead of the native equations of state ω_Λ, we show that this model cannot accommodate any transition from the dark energy with to the phantom regime . Furthermore, the case of interaction between four-dimensional cold dark matter and five-dimensional cold dark matter is considered for completeness. Here we find that the redshift of matter-radiation equality z_eq is the same order as . Finally, we obtain a general decay rate Γ which is suitable for describing all interactions.

The present-day accelerated expansion of the universe is naturally addressed within the Brans–Dicke theory just by using holographic dark energy model with inverse of Hubble scale as IR cutoff and power law temporal behavior of scale factor. It is also concluded that if the universe continues to expand, then one day it might be completely filled with dark energy.

In this paper, the holographic dark energy in Brans–Dicke theory is confronted by cosmic observations from SN Ia, BAO, OHD and CMB via Markov-Chain Monte-Carlo (MCMC) method. The best fit parameters are found in 1σ region: and (equivalently ω = 2415.653 which is less than the solar system bound and consistent with other constraint results). With these best fit values of the parameters, it is found that the universe is undergoing accelerated expansion, and the current value of equation of state of holographic dark energy which is phantom like in Brans–Dicke theory. The effective Newton's constant decreases with the expansion of our universe for the negative value of model parameter α.

Motivated by the work: K. Karami and J. Fehri, Phys. Lett. B684, 61 (2010) and A. Sheykhi, Phys. Lett. B681, 205 (2009), we generalize their work to the new holographic dark energy model with in the framework of Brans–Dicke cosmology. Concretely, we study the correspondence between the quintessence, tachyon, K-essence, dilaton scalar field and Chaplygin gas model with the new holographic dark energy model in the non-flat Brans–Dicke universe. Furthermore, we reconstruct the potentials and dynamics for these models. By analysis we can show that for new holographic quintessence and Chaplygin gas models, if the related parameters to the potentials satisfy some constraints, the accelerated expansion can be achieved in Brans–Dicke cosmology. In particular, the counterparts of fields and potentials in general relativity can describe accelerated expansion of the universe. It is worth stressing that not only can we give some new results in the framework of Brans–Dicke cosmology, but also the previous results of the new holographic dark energy in Einstein gravity can be included as special cases given by us.

In the original holographic dark energy (HDE) model, the dark energy density is proposed to be , with c a dimensionless constant characterizing the properties of the HDE. In this work, we propose the generalized holographic dark energy (GHDE) model by considering the parameter c as a redshift-dependent function c(z). We derive all the physical quantities of the GHDE model analytically, and fit the c(z) by trying four kinds of parametrizations. The cosmological constraints of the c(z) are obtained from the joint analysis of the present SNLS3+BAO+CMB+H₀ data. We find that, compared with the original HDE model, the GHDE models can provide a better fit to the data. For example, the GHDE model with JBP-type c(z) can reduce the of the HDE model by 2.16. We also find that, unlike the original HDE model with a phantom-like behavior in the future, the GHDE models can present many more different possibilities, i.e. it allows the GHDE in the future to be either quintessence-like, cosmological constant-like, or phantom-like, depending on the forms of c(z).

We investigate a spatially flat Friedmann–Robertson–Walker (FRW) universe where dark matter exchanges energy with a self-interacting holographic dark energy (SIHDE). Using the χ²-statistical method on the Hubble function, we obtain a critical redshift that seems to be consistent with both BAO and CMB data. We calculate the theoretical distance modulus for confronting with the observational data of SNe Ia for small redshift z ≤ 0.1 and large redshift 0.1 ≤ z ≤ 1.5. The model gets accelerated faster than the ΛCDM one and it can be a good candidate to alleviate the coincidence problem. We also examine the age crisis at high redshift associated with the old quasar APM 08279+5255.

This paper is devoted to study the power-law entropy corrected holographic dark energy (ECHDE) model in the framework of f(T) gravity. We assume infrared (IR) cutoff in terms of Granda–Oliveros (GO) length and discuss the constructed f(T) model in interacting as well as in non-interacting scenarios. We explore some cosmological parameters like equation of state (EoS), deceleration, statefinder parameters as well as ω_T–ω_T′ analysis. The EoS and deceleration parameters indicate phantom behavior of the accelerated expansion of the universe. It is mentioned here that statefinder trajectories represent consistent results with ΛCDM limit, while evolution trajectory of ω_T–ω_T′ phase plane does not approach to ΛCDM limit for both interacting and non-interacting cases.

The paper deals with a dynamical system analysis of the cosmological evolution of an holographic dark energy (HDE) model interacting with dark matter (DM) which is chosen in the form of dust. The infrared cutoff of the holographic model is considered as future event horizon or Ricci length scale.

The interaction term between dark energy (DE) and DM is chosen of following three types: (i) proportional to the sum of the energy densities of the two dark components, (ii) proportional to the product of the matter energy densities and (iii) proportional to DE density.

The dynamical equations are reduced to an autonomous system for the three cases and corresponding phase space is analyzed.

The motivation of this paper is to study the bulk viscosity effect in Ricci dark energy (RDE) model within the framework of modified f(R, T) gravity, where R is the Ricci scalar and T is the trace of the energy–momentum tensor. As most studies assume that the universe is filled with a perfect fluid, viscosity is expected to present at least during some stages, especially in the early stage of the evolution of the universe but it could still become significant in the future. We assume the universe is filled with viscous RDE and pressureless dark matter. We consider the total bulk viscous coefficient is in the form of $\zeta ={\zeta }_0+{\zeta }_1$H, where ${\zeta }_0$ and ${\zeta }_1$ are the constants. We obtain the solutions to the modified field equations by assuming a form f(R, T) = R$+\lambda$T, where $\lambda$ is a constant. We find the scale factor and deceleration parameter, and classify all possible evolutions of the universe. We briefly discuss the future finite-time singularity and show that the Big Rip singularity appears in viscous RDE model. We investigate two geometrical diagnostics, statefinder parameter and Om to analyze the dynamics of evolution of the universe. The trajectories of statefinder parameter reveal that the model behaves like quintessence for small $\zeta$, and for large $\zeta$ it shows the Chaplygin gas-like. However, in late time both the models approach $\mathrm{\Lambda }$CDM. The model shows a transition from decelerated phase to accelerated phase. Similarly, the Om analysis reveals that the model behaves like quintessence for small $\zeta$ and phantom-like for large $\zeta$. We extend our study to analyze the time evolution of the total entropy and generalized second law of thermodynamics of viscous RDE model in f(R, T) theory inside the apparent horizon. Our study shows that the generalized second law of thermodynamics always preserves in viscous RDE model in a region enclosed by the apparent horizon under the suitable constraints of viscous coefficients.

This work deals with dynamical system analysis of Holographic Dark Energy (HDE) cosmological model with different infra-red (IR)-cutoff. By suitable transformation of variables, the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by Center Manifold Theory and Lyapunov function method. Possible bifurcation scenarios have also been explained.

We study the cosmological consequences of interacting Tsallis holographic dark energy model in the framework of the fractal universe in which the Hubble radius is considered as the IR cutoff. We derive the equation of state (EoS) parameter, deceleration parameter and the evolution equation for the Tsallis holographic dark energy density parameter. Our study shows that this model can describe the current accelerating universe in both non-interacting and interacting scenarios, and also a transition occurs from the deceleration phase to the accelerated phase at the late-time. Finally, we check the compatibility of free parameters of the model with the latest observational results by using the Pantheon supernovae data, eBOSS, 6df, BOSS DR12, CMB Planck 2015, Gamma-Ray Burst.

By using the holographic hypothesis and Kaniadakis generalized entropy, which is based on relativistic statistical theory and modified Boltzmann–Gibbs entropy, we build Kaniadakis holographic dark energy (DE) model in the Brans–Dicke framework. We derive cosmological parameters of the Kaniadakis holographic DE model, with IR cutoff as the Hubble horizon, in order to investigate its cosmological consequences. Our study shows that even in the absence of an interaction between the dark sectors of the cosmos, the Kaniadakis holographic dark energy model with the Hubble radius as IR cutoff can explain the present accelerated phase of the universe expansion in the Brans–Dicke theory. The stability of the model, using the squared of sound speed, has been checked and it is found that the model is unstable in non-interacting case and can be stable for some range of model parameters within the interacting case.

We study the holographic dark energy (HDE) with adiabatic matter creation process to explain the present-day accelerated expansion of the Universe. The field equations are discussed and solved analytically for various cosmological parameters such as the Hubble parameter, deceleration parameter and effective equation of state parameter in terms of redshift by considering a more general form of the matter creation rate. The viability of such model is checked using the recent data of Type Ia supernovae Pantheon sample, Hubble function $H(z)$ data, joined data of baryon acoustic oscillations/cosmic microwave background and latest local $H_0$ by SH0ES. We achieve the most fitting values of model parameters by performing the statistical analysis of our model with the three different combination of data sets. The HDE model, with IR cutoff as Hubble horizon, in the absence of matter creation does not show phase transition. While the induction of matter creation to the same model shows the recent transition from a decelerating to an accelerated phase. Our outcomes show that the model with matter creation is compatible with the data sets used. We find that the HDE model with matter creation provides the Hubble function which matches sufficiently well with the observed Hubble data. Finally, we perform geometrical and cosmographic analyses to explicate our model and compare it with the other dark energy models like $\mathrm{\Lambda }$CDM model. It is found that the evolution of model starts from Chaplygin gas region in early times, enters into quintessence region in medieval time and finally approaches to $\mathrm{\Lambda }$CDM model.

This work deals with the newly approached extended $f(P)$ cubic gravity in a cosmological background where $P$ denotes the cubic gravity. Here, we peruse the cosmological nature of the different types of dark energy candidates in the framework of $f(P)$ gravity. Next, we study the reconstruction scenario of $f(P)$ gravity model according to ordinary holographic dark energy, ordinary new agegraphic dark energy, entropy-corrected holographic dark energy in power-law and logarithmic versions and entropy-corrected new agegraphic dark energy in power-law and logarithmic versions with two classes of the scale factor. We derive different forms of the unknown function $f(P)$ in the context of these dark energy candidates. By the trajectories of the EoS parameter $w_P$, all models give evidence of their candidature for the explanation of the phantom regime and also the quintessence regime in the late stage of the universe. Also, the stability condition ensures that our reconstructed models are classically stable.

In this paper, we investigate the Rényi holographic dark energy model with the interaction between dark energy and dark matter within the framework of the fractal cosmology in which the Hubble horizon is considered as the IR cutoff. In this setting, we derive the evolution equation of the Rényi holographic dark energy density parameter, the equation of state (EoS) parameter and deceleration parameter. We find that the model in the fractal cosmology can explain the accelerated expansion of the universe. In addition, we discuss the statefinder diagnosis of this model, plotting the curves of $r$ and $s$ with redshift $z$ and the evolutionary trajectories of $r-s$. We find that statefinder can ideally break the degeneracy of different coupling parameter values in this model. Moreover, we find that the statefinder pair $S_3^{(2)}$ performs better than $S_3^{(1)}$ and $r-s$ in this model.

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. $Q_1=3H\xi {\rho }_{\mathrm{\text{de}}}$, $Q_2=3H\xi {\rho }_{\mathrm{\text{dm}}}$, $Q_3=3H\xi {\rho }_{{\mathrm{\text{de}}}^2}/({\rho }_{\mathrm{\text{de}}}+{\rho }_{\mathrm{\text{dm}}})$, $Q_4=3H\xi {\rho }_{{\mathrm{\text{dm}}}^2}/({\rho }_{\mathrm{\text{de}}}+{\rho }_{\mathrm{\text{dm}}})$ 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 $\mathrm{\Lambda }$CDM model, this paper also geometrically diagnoses the model with the two ways of Statefinder hierarchy and Om$(z)$. From their respective evolution image you can see, these two kinds of diagnosis methods can not only distinguish different from $\mathrm{\Lambda }$CDM model, but also can intuitively reflect the coupling parameters that can significantly affect the dark energy model.

We investigate both the interacting and non-interacting Rényi Holographic Dark Energy (RHDE) models in Dvali–Gabadadze–Porrati (DGP) braneworld framework. Cosmological parameters and their evolutions are probed to obtain realistic cosmological models. We note that both the models accommodate the present accelerating phase of expansion with the observed dark energy density. Classical stability of the cosmological model and Om-diagnostic are also studied to test the suitability of the cosmological models obtained in the presence of RHDE in DGP braneworld.

In this paper, we study two different dynamic structures of holographic dark energy, namely Tsallis and Kaniadakis, within the framework of Brans–Dicke cosmology. We consider the complex form of the quintessence model and examine both non-interacting and interacting cases, calculating various cosmological parameters such as the equation of state $\omega$ and discussing the behavior of $\omega -{\omega }^{\prime }$. We modify the potential and study the scalar field dynamics of complex quintessence cosmology. Additionally, we examine the effects of the two parts of the quintessence field (real and complex) and the fractional energy density ${\mathrm{\Omega }}_D$, determining whether they can describe a real universe. We note that the fractional energy density cannot be arbitrary between 0 and 1, as it depends on the Tsallis, Kaniadakis and Brans–Dicke cosmology-free parameters. For each model, we establish a relationship between the fractional energy density and other parameters such as $\delta$, $b^2$, $\alpha$ and $\beta$.