Narrow Results

In this paper, we investigate the validity of the generalized second law of thermodynamics (GSLT) in the DGP braneworld. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon or the event horizon. The universe is chosen to be homogeneous and isotropic and the validity of the first law has been assumed here. The matter in the universe is taken in the form of non-interacting two-fluid system: one component is the holographic dark energy and the other component is in the form of dust.

The illustration of cosmic acceleration is being presented in the framework of DGP braneworld and dynamical Chern–Simons modified gravity in the presence of casual Israel–Stewart formalism. In this way, we discuss the evolution parameter which leads to the accelerated expansion of the universe in the phantom as well as quintessence region for both gravities. The squared speed of sound $\left({v_s}^2\right)$ leads to the stable behavior of the current physical system in both gravities in the later epoch. Also, the entropy variation, as well as thermal equilibrium condition, remains valid in both frameworks at the present and later epoch.

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.

The cosmological analysis is being studied in the present work in Dvali–Gabadadze–Porrati (DGP) braneworld scenario by taking various interacting modified holographic dark energy (HDE) models. We discuss the various cosmological parameters such as deceleration parameter, equation-of-state (EoS) parameter and squared speed of sound. It is found that the trajectories of deceleration parameter exhibit in accelerated phase of the universe for all models. The EoS parameter corresponds to various phases of cosmic acceleration like quintessence, vacuum, phantom and also exhibits consistency with observational data. The squared speed of sound also gives stability of models in the current scenario. The ${\omega }_{\vartheta }-{\omega }_{\vartheta }^{\prime }$ also gives consistent results with various observational schemes. The statefinders plane also exhibits the cosmic acceleration. It is interesting to remark here that some of our results shows consistency with observational data like WMAP+CMB+BAO+$H_0$+SNe.

In this paper, we present a model for the late-time evolution of the universe where a dark energy-dark matter interaction is invoked. Dark energy is modeled through an holographic Ricci dark energy component. The model is embedded within an induced gravity braneworld model. For suitable choices of the interaction coupling, the big rip and little rip induced by the holographic Ricci dark energy, in a relativistic model and in an induced gravity braneworld model, are removed. In this scenario, the holographic dark energy will have a phantom like behavior even though the brane is asymptotically de Sitter.