Pankaj Kumar

In this work, we examine the cosmological viability of an accelerating Brans–Dicke universe in the presence of Tsallis holographic dark energy, extending earlier study that employed a logarithmic form of the Brans–Dicke scalar field in a spatially flat Friedmann–Robertson–Walker space–time. While previous analysis has primarily focused on late–time acceleration, we investigate both early and late–time cosmic evolution within this framework. The dynamical behavior of the deceleration and equation–of–state parameters is analyzed to assess whether the model can qualitatively reproduce the known expansion history of the universe, including an inflationary phase and the subsequent decelerated era. We further examine the evolution of the matter to dark energy density ratio and find that it varies sufficiently slowly at late times, indicating a soft alleviation of the cosmic coincidence problem. In addition, the generalized second law of thermodynamics is employed as a consistency test to assess the thermodynamic viability of the model during different evolutionary epochs. The standard energy conditions are also investigated as consistency checks rather than as sources of novel phenomenology. Our results indicate that the considered Tsallis holographic dark energy scenario within Brans-Dicke theory provides a self-consistent and analytically tractable framework for describing the qualitative features of cosmic evolution.

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.

In this paper, we present a comprehensive analysis of the holographic dark energy model with Granda–Oliveros cutoff in Brans–Dicke theory. We assume that the scalar field has a logarithmic form [ ], where a is the scale factor, [ ] and [ ] are arbitrary constants. The evolution of the universe is discussed by calculating the equation of state parameter [ ] of holographic dark energy and deceleration parameter q. To discuss the cosmography of the model, we calculate the value of the Hubble parameter [ ] and constrain the model parameters using recent observational data sets. The best fit value of Hubble constant [ ] has been obtained which shows agreement with the recent observations. We plot graphs of [ ] and q using the best fit values of the parameters which depict their evolution against the redshift parameter z. The graphs show that the model explains the recent phase transition of the universe. We observe an interesting result which shows a decelerating universe in the far future. It is observed that [ ] does not cross the phantom divide line, i.e. the model is free from a big-rip singularity. The statefinder analysis shows, however, the model trajectory lies in the quintessence region for quite a long period, but the overall evolution is different from known dark energy models. We apply a thermodynamic analysis and find that the generalized second law of thermodynamics holds in the model for the best fit values of the parameters. We verify the stability of the model using the squared sound speed method and find that the model is stable. Moreover, we study the energy conditions for the present model. We observe that the strong energy condition is violated during the present epoch and in the future. However, we observe that it is again satisfied in the vicinity of the point [ ]. The null energy condition remains satisfied throughout which shows consistency with the behavior observed in the [ ]-CDM model.

In this paper, we present a model of inflation in the original form of Brans–Dicke (BD) theory without any modification and without adding any dark energy candidate. We consider a log function of the scale factor in the BD scalar field to discuss the inflationary era of the universe. We obtain the expressions for the deceleration parameter and the equation of state parameter, and plot their graphs against the cosmic scale factor. We observe that the universe starts with decelerated expansion and experiences an early time phase transition from a decelerated phase to an accelerated phase. After a very short period, the accelerated expansion ends in a decelerated expansion, showing the inflationary era of the cosmic evolution. To analyze the model on thermodynamic ground, we consider generalized second law of thermodynamics and observe that the law is satisfied within the model. Further, we study the stability of the model using the squared sound speed method. We plot the squared sound speed against cosmic time t and discuss the effects of the parameters on the stability of the model. We observe that for suitable values of the model parameters our model is stable.

In this paper, we reconsider the concept of bulk viscosity in Brans–Dicke theory to study accelerated expansion of the universe in a flat Friedmann–Robertson–Walker metric. In recent works on bulk viscosity in Brans–Dicke theory, the power-law form of Brans–Dicke scalar field has been taken to explain recent phase transition of the universe, however, power-law form confronts constant deceleration parameter problem. Therefore, we consider recently proposed well-motivated logarithmic form of Brans–Dicke scalar field to discuss bulk viscous model in Brans–Dicke theory. We obtain the values of deceleration parameter and equation of state parameter for the model, and plot their graphs against the redshift parameter z. The plots show that the model is able to explain the recent phase transition of the universe and equation of state parameter shows the behavior of dark energy. Further, we apply two important analysis, namely, [ ] analysis and thermodynamic analysis to examine our model. The [ ] analysis shows that our model belong to thawing region and shows similarities with quintessence model. All the trajectories start from the point [ ] with different negative values of w having quintessence behavior. The thermodynamic analysis shows that the model satisfies generalized second law of thermodynamics.