Interacting Ghost Dark Energy with Sign-Changeable Coupling in Brans-Dicke Cosmology

TL;DR

The paper investigates ghost dark energy within Brans-Dicke cosmology in a flat FRW universe, incorporating a sign-changeable DM–DE coupling and a logarithmic Brans-Dicke scalar field. By deriving the BD field equations and continuity relations with $\rho_D = \gamma H$ and $Q = 3 b^2 H q \rho_D$, it analyzes the evolution of the equation of state $w_D$ and the deceleration parameter $q$, along with the $w_D-w'_D$ diagnostic and horizon thermodynamics. The results show $w_D$ can be quintessence-like or phantom-like, the universe undergoes a recent transition to acceleration and may experience a future deceleration, and the generalized second law is satisfied, indicating thermodynamic consistency. The work offers a dynamical DE framework within BD gravity with rich phenomenology and potential observational implications, while acknowledging that full data-fitting remains for future work.

Abstract

In this study, we analyze the ghost dark energy model in Brans-Dicke cosmology in the framework of a flat Friedmann-Lemaitre-Robertson-Walker universe. We consider an interaction between ghost dark energy and dark matter with a sign-changeable interaction term. To discuss the cosmological implications of the model, we consider a well-motivated logarithmic form of the Brans-Dicke scalar field. By deriving the cosmological evolution equations, we obtain the cosmological parameters such as the equation of state and deceleration parameters. We analyze the behavior of the cosmological parameters by plotting their graphs against the redshift parameter ($z$). We observe that the equation of state parameter shows quintessence-like behaviour during present and future epochs; however, phantom-like behavior is also possible for suitable values of the model parameters. Analysis of the deceleration parameter shows a smooth recent phase transition of the universe (deceleration to acceleration). An interesting result we observe is the decelerated expansion of the universe in the far future, i.e, the universe experiences another phase transition in the future. The physical significance of the well-known cosmological plane ($w_D-w_D'$ plane) is discussed in our model. We observe that the trajectories start in the freezing region with the same initial behavior, deviate from each other during the evolution and ends in the thawing region. Finally, we perform a detailed thermodynamic analysis and demonstrate that the generalized second law of thermodynamics is satisfied within the present interacting ghost dark energy model.

Figures (4)

• Figure 1: We have taken $H=70$, $\phi_0=1$, $b=0.4$ and $\gamma=6$ to plot $w_D$ against $z$. Fig.(a) is plotted for fixed values $\omega=-100$, $\beta=1$ and for various values of $\alpha$. Fig.(b) is plotted for fixed values $\omega=-100$, $\alpha=2.5$ and for various values of $\beta$. Fig.(c) is plotted for fixed values $\alpha=2.5$, $\beta=1$ and for various values of $\omega$. Fig.(d) is plotted for fixed values $\alpha=2.5$, $\beta=1$, $\omega= -100$ and for various values of $\gamma$.
• Figure 2: We have taken $H=70$, $\phi_0=1$ and $b=0.4$ to plot $q$ against $z$. Fig.(a) is plotted for fixed values $\omega=-100$, $\beta=1$, $\gamma=6$ and for various values of $\alpha$. Fig.(b) is plotted for fixed values $\omega=-100$, $\alpha=2.5$, $\gamma=6$ and for various values of $\beta$. Fig.(c) is plotted for fixed values $\alpha=2.5$, $\beta=1$, $\gamma=6$ and for various values of $\omega$. Fig.(d) is plotted for fixed values $\alpha=2.5$, $\beta=1$, $\omega= -100$ and for various values of $\gamma$.
• Figure 3: We have plotted trajectories in $w_{D}-w_{D}'$ plane and have taken fixed values of $\phi_0= 1$, $H= 70$, $\gamma= 6$, $b= 0.4$. The trajectories are plotted for various values of parameters $\alpha$, $\beta$ and $\omega$. The trajectory 1 has been plotted for $\alpha = 2.4$, $\beta = 1.5$, $\omega = -90$. We have taken $\alpha = 2.2$, $\beta = 1.8$, $\omega = -100$ to plot trajectory 2. The trajectory 3 has been plotted for $\alpha = 2.5$, $\beta = 1.6$, $\omega = -120$.
• Figure 4: To plot the $\dot{S}_{\text{tot}}$ trajectories, we have taken $H=70$, $\phi_0=1$, $b=0.4$ and $\gamma=6$. The trajectories are plotted for various values of parameters $\alpha$, $\beta$ and $\omega$.