A Cosmological Analysis of Barrow Holographic Dark Energy Cosmological model within Brans-Dicke Gravity

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 [Formula: see text], where a is the scale factor, [Formula: see text] and [Formula: see text] are arbitrary constants. The evolution of the universe is discussed by calculating the equation of state parameter [Formula: see text] of holographic dark energy and deceleration parameter q. To discuss the cosmography of the model, we calculate the value of the Hubble parameter [Formula: see text] and constrain the model parameters using recent observational data sets. The best fit value of Hubble constant [Formula: see text] has been obtained which shows agreement with the recent observations. We plot graphs of [Formula: see text] 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 [Formula: see text] 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 [Formula: see text]. The null energy condition remains satisfied throughout which shows consistency with the behavior observed in the [Formula: see text]-CDM model.

We have constructed a dark energy cosmological model in the framework of the generalized Brans Dicke (GBD) theory with a self-interacting potential. The source of dark energy is considered through a unified dark fluid (UDF) characterized by a linear equation of state (EoS). A time-varying deceleration parameter simulating the cosmic transit behavior has been introduced to get the dynamical behavior of the model. The $$H(z)$$ data have been explored to constrain the model parameters and to study the dynamical aspects of the Brans-Dicke parameter and the scalar field.

We study a holographic dark energy model in the framework of Brans-Dicke (BD) theory with taking into account the interaction between dark matter and holographic dark energy. We use the recent observational data sets, namely SN Ia compressed Joint Light-Analysis(cJLA) compilation, Baryon Acoustic Oscillations (BAO) from BOSS DR12 and the Cosmic Microwave Background (CMB) of Planck 2015. After calculating the evolution of the equation of state as well as the deceleration parameters, we find that with a logarithmic form for the BD scalar field the phantom crossing can be achieved in the late time of cosmic evolution. Unlike the conventional theory of holographic dark energy in standard cosmology ($\omega_D=0$), our model results a late time accelerated expansion. It is also shown that the cosmic coincidence problem may be resolved in the proposed model. We execute the statefinder and Om diagnostic tools and demonstrate that interaction term does not play a significant role. Based on the observational data sets used in this paper it seems that the best value with $1\sigma$ and $2\sigma$ confidence interval are $\Omega_m=0.268^{+0.008~+0.010}_{-0.007~-0.009}$, $ \alpha=3.361^{+0.332~+0.483}_{-0.401~-0.522}$, $\beta=5.560^{+0.541~+0.780}_{-0.510~-0.729}$, $c=0.777^{+0.023~+0.029}_{-0.017~-0.023}$ and $b^2 =0.045$, according to which we find that the proposed model in the presence of interaction is compatible with the recent observational data.

Geodesic deviation equation in Brans–Dicke theory in arbitrary dimensions

The pure Brans-Dicke (BD) gravity with or without the cosmological constant $\Lambda $ has been taken as a model theory for the dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity where Newton's constant is strictly a ``constant'' having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies which actually is not the case.

The pure Brans-Dicke (BD) gravity with or without the cosmological constant Λ has been taken as a model theory for dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of a dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity, where Newton’s constant is strictly a “constant” having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies, which actually is not the case.

In this paper, we have generalized the behaviors of transit cosmological model under the observational data with Barrow holographic dark energy. We consider the scale factor field as [Formula: see text] to get exact solutions for the field equations in a non-flat FRW universe in Brans–Dicke theory. The values of the model parameters [Formula: see text] and [Formula: see text] are obtained by best fitting of 46 observational Hubble data (OHD) points in the range [Formula: see text]. The derived model exhibits a transition scenario for open, flat and closed universe. The EoS parameter shows a quintom-like behavior, lies both quintessence ([Formula: see text]) and phantom ([Formula: see text]) regions and crosses the phantom divide. The matter and dark energy density parameters [Formula: see text], scalar field [Formula: see text] and other cosmological parameters provide the results consistent with the recent observational datasets. Some other physical and geometrical behaviors of BHDE are also described and the satisfactory behaviors are found with current observations (OHD+JLA).

Both dark energy and the thermodynamics on apparent horizon in cosmology have been broadly investigated in recent several years. In order to maintain the continuity equation of the total matter in the universe, a new interacting dark energy in the framework of Brans-Dicke theory is proposed. Considering this new interacting dark energy, an equilibrium thermodynamics in Brans-Dicke theory is constructed successfully. Moreover, this new interacting dark energy can be regarded as arising from the “Holographic Dark Energy” models.

Holographic dark energy

We show that Brans-Dicke (BD) theory in 5D may explain the present cosmic accelerated expansion without recurring to matter fields in 5D or dark energy in 4D. Without making any assumption on the nature of the extra coordinate or the matter content in 5D, here we demonstrate that the vacuum BD field equations in 5D are equivalent, on every hypersurface orthogonal to the extra dimension, to a BD theory in 4D with a self interacting potential and an effective matter field. The potential is not introduced by hand, instead the reduction procedure provides an expression that determines its shape up to a constant of integration. It also establishes the explicit formulae for the effective matter in 4D. In the context of FRW cosmologies, we show that the reduced BD theory gives rise to models for accelerated expansion of a matter-dominated universe which are consistent with current observations and with a decelerating radiation-dominated epoch.

We investigate the interacting holographic dark energy (HDE) with Granda–Oliveros (GO) infrared (IR)-cutoff in the framework of Brans–Dicke (BD) cosmology. We obtain the equation of state (EoS) parameter of HDE, wD, the effective EoS parameter w eff , the deceleration parameter q and the squared of sound speed [Formula: see text] in a flat Friedmann–Robertson–Walker (FRW) universe. We show that at late-time the cosmic coincidence problem can be alleviated. Also we show that for noninteracting case, HDE can give a unified dark matter–dark energy (DM–DE) profile in BD cosmology, except that it cannot solve the coincidence problem in the future. By studying the EoS parameter, we see that the phantom divide may be crossed. Using the latest observational data, we calculate the best values of the parameters for interacting HDE in BD framework. Computing the deceleration parameter implies that the transition from deceleration to the acceleration phase occurred for redshift z ≥ 0.5. Finally, we investigate the sound stability of the model, and find that HDE with Granda–Oliveros (GO)-cutoff in the framework of BD cosmology can lead to a stable DE-dominated universe favored by observations, provided we take β = 0.44 and b2 < 0.35. This is in contrast to HDE model in Einstein gravity which does not lead to a stable DE-dominated universe.

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: [Formula: see text] and [Formula: see text] (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 [Formula: see text] 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.

Isotropic and homogeneous cosmological models with a perfect fluid cource in Brans-Dicke theory are investigated from the point of view of dynamical system theory.

The evolution of universe in Brans-Dicke (BD) theory is discussed in this paper. Considering a parameterized scenario for BD scalar field $\phi=\phi_{0}a^{\alpha}$ which plays the role of gravitational "constant" $G$, we apply the Markov Chain Monte Carlo method to investigate a global constraints on BD theory with a self-interacting potential according to the current observational data: Union2 dataset of type supernovae Ia (SNIa), high-redshift Gamma-Ray Bursts (GRBs) data, observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. It is shown that an expanded universe from deceleration to acceleration is given in this theory, and the constraint results of dimensionless matter density $\Omega_{0m}$ and parameter $\alpha$ are, $\Omega_{0m}=0.286^{+0.037+0.050}_{-0.039-0.047}$ and $\alpha=0.0046^{+0.0149+0.0171}_{-0.0171-0.0206}$ which is consistent with the result of current experiment exploration, $\mid\alpha\mid \leq 0.132124$. In addition, we use the geometrical diagnostic method, jerk parameter $j$, to distinguish the BD theory and cosmological constant model in Einstein's theory of general relativity.

Unified dark fluid and cosmic transit models in Brans–Dicke theory