Five-dimensional Brans–Dicke compactified universe dominated by a varying speed of light

In this paper, we study three scalar fields, namely the quintessence, phantom, and tachyon fields, to explore the source of dark energy via the Gaussian processes method from the background and perturbation growth rate data. The corresponding reconstructions suggest that the dark energy should be dynamical. Moreover, the quintom field, which is a combination of the quintessence and phantom fields, is powerfully favored by the reconstruction. The mean values indicate that the potential in the quintessence field is a double exponential function, whereas in the phantom field is a double Gaussian function. This reconstruction can provide an important reference for the scalar field study. The two types of data employed reveal that the tachyon field is disadvantageous for describing the cosmic acceleration.

In this letter, we have considered the universe is filled with the mixture of tachyonic field and scalar or phantom field. If the tachyonic field interacts with scalar or phantom field, the interaction term decays with time and the energy for scalar field is transferred to tachyonic field or the energy for phantom field is transferred to tachyonic field. The tachyonic field and scalar field potentials always decrease, but phantom field potential always increases.

Hubble tension between the local measurement and global observation has been a key problem in cosmology. In this paper, we consider the quintessence scalar field, phantom field and quintom field as the dark energy to reconcile this problem. Different from most previous work, we start from the dimensionless equation of state (w) of dark energy, not a parameterization of potential. The combined analysis shows that observational data sets favor Hubble constant H0=71.3−0.917+0.854kms−1Mpc−1 , which can reconcile Hubble tension within 1.20σ. We also perform a Bayes factor analysis using the MCEvidence code, and confirm that the phantom scalar field is still the most effective. To investigate the reason of Hubble tension, we analyze the density parameter. The comparison shows that the scalar fields provide a slightly larger Ω b h 2 and smaller Ω c h 2 than the standard ΛCDM model. We finally analyze a possible reason of Hubble tension from the kinematic acceleration ä . We find an interesting physical phenomenon. The acceleration ä in these scalar fields are similar as the ΛCDM model at about redshift z > 0.5. However, they increase and deviate from each other at low redshift, especially in the near future. Only the ä in phantom scalar field will decrease in the future.

The generalized f(R) gravity with coupling in five-dimensional (5D) spacetime is studied on the basis of both the 4D generalized f(R) gravity with coupling and the pure f(R) gravity without coupling in 5D spacetime. Specifically, by assuming a hypersurface-orthogonal space-like Killing vector field in 5D spacetime, the generalization of the 4D generalized f(R) gravity to 5D can be realized, which can give the reduced 4-metric coupled with two scalar fields. In particular, we discuss a special class of models, i.e., f1(R) = f2(R) = αRm (m ≠ 1), and choose B(Lm) = Lm = −ρ in the homogeneous and isotropic cosmology with the 4D Friedmann—Robertson—Walker metric. The numerical analysis shows that the parameter m can be constrained by means of the current observations for the deceleration parameter, which implies that this generalized f(R) model with coupling in 5D spacetime can account for the present accelerated expansion of the universe.

In the present work, we consider the tachyonic field, the phantom field, and the scalar field in both interacting and non-interacting situations and investigate the validity of the generalized second law of thermodynamics in a flat FRW universe. We find that in all cases, except for the phantom field dominated universe, the derivative of the entropy remains at negative level and increases with the decrease in redshift.

The dark side of the universe is mysterious and its nature is still unknown. In fact, this poses perhaps as the biggest challenge in the modern cosmology. The two components of the dark sector (dark matter and dark energy) correspond today to around ninety five percent of the universe. The simplest dark energy candidate is a cosmological constant. However, this attempt presents a huge discrepancy of 120 orders of magnitude between the theoretical prediction and the observed data. Such a huge disparity motivates physicists to look into a more sophisticated models. This can be done either looking for a deeper understanding of where the cosmological constant comes from, if one wants to derive it from first principles, or considering other possibilities for accelerated expansion, such as modifications of general relativity, additional matter fields and so on. Still regarding a dynamical dark energy, there may exist a possibility of interaction between dark energy and dark matter, since their densities are comparable and, depending on the coupling used, the interaction can also alleviate the issue of why dark energy and matter densities are of the same order today. Phenomenological models have been widely explored in the literature. On the other hand, field theory models that aim a consistent description of the dark energy/dark matter interaction are still few. In this thesis, we explore either a scalar or a vector field as a dark energy candidate in several different approaches, taking into account a possible interaction between the two components of the dark sector. The thesis is divided in three parts, which can be read independently of each other. In the first part, we analyze the asymptotic behavior of some cosmological models using either scalar or vector fields as dark energy candidates, in the light of the dynamical system theory. In the second part, we use a scalar field in the supergravity framework to build a model of dynamical dark energy and also to embed a holographic dark energy model into minimal supergravity. Finally, in the third part, we propose a model of metastable dark energy, in which the dark energy is a scalar field with a potential given by the sum of even self-interactions up to order six. We insert the metastable dark energy into a dark SU (2) R model, where the dark energy doublet and the dark matter doublet naturally interact with each other. Such an interaction opens a new window to investigate the dark sector from the point-of-view of particle physics.

A relativistic theory including two types of gravitation, tensor and scalar field, has recently been published by Zhang, providing the origin of the Hubble tension as well as that of the cosmological constant. It is shown here that the combination of scalar and tensor fields enables the relativistic theory to be compatible with Mach's principle (MP). The scalar field can also act as an inflation field at the cosmic inflationary era and convert to dark matter particles during its oscillating era. As the quanta of the excitation states of the scalar field, unlike ordinary matter, this type of dark matter does not couple to the equilibrium state of the scalar field. The masses of the quanta are estimated to be less than 31 meV if we assume that all dark matter is of this type. The most probable mass is 2 meV. Due to the dynamic equilibrium state of the scalar field acting as dark energy, a simulated equation of state is introduced for this dynamical dark energy. Consequently, if the true space of the Universe is closed, observers who are based on the assumption of flat space would discover that the equation of state for dark energy has ever crossed $\ensuremath{-}1$ in the near past. Since Dark Energy Spectroscopic Instrument Data (DESI) imply that the equation of state may cross $\ensuremath{-}1$, then the spatial curvature of our Universe may be positive based on the gravitational scheme. These effects above are analyzed in the frame of general relativity (GR) by canonically subsuming the canonical scalar field into GR. It is also demonstrated that the new interaction between the scalar field and ordinary matter can be independently analyzed in the frame of special relativity (SR). The equations of motion of several given matter fields in the presence of the scalar gravitational field are obtained in SR frame. Unlike the GR effect of the self-interaction potential of the scalar field accelerating the expansion rate of the Universe, the so-called scalar-field-mediating force is caused by the gradient of the scalar field and is entirely an effect of SR, independent of GR. We refer to this new interaction as scalar gravitation to distinguish it from Einstein's tensor gravitation. Since all ordinary matter couples to the scalar field in the same conformal way, the scalar field can result in forces not only between fermions but also bosons. Due to the spontaneous-symmetry-breaking of the coupling, the matter-density-dependent forces are often short ranged. In the current density of the Universe, the range of interaction is estimated to be 2.2 \ensuremath{\mu}m if all dark matter is attributed to the excitation of the scalar field. When the Lorentz invariant effective nonrelativistic energy density ${\ensuremath{\rho}}_{\mathrm{N}}=\ensuremath{\rho}\ensuremath{-}3P$ of the ordinary matter fluid decreases (which does not necessarily mean that the energy density $\ensuremath{\rho}$ of the fluid must be low because the fluid pressure $P$ can be high enough to make ${\ensuremath{\rho}}_{\mathrm{N}}=0$), the range of interaction will increase as a function of $1/\sqrt{{\ensuremath{\rho}}_{\mathrm{N}}}$. Thus, the scalar-mediated force will play a crucial role in the formation of galaxies, especially under relativistic conditions and extremely low energy densities of ordinary matter.

We consider a 5-dimensional scalar-tensor theory which is a direct generalization of the original 4-dimensional Brans-Dicke theory to 5-dimensions. By assuming that there is a hypersurface-orthogonal spacelike Killing vector field in the underlying 5-dimensional spacetime, the theory is reduced to a 4-dimensional theory where the 4-metric is coupled with two scalar fields. The cosmological implication of this reduced theory is then studied in the Robertson-Walker model. It turns out that the two scalar fields may account naturally for the present accelerated expansion of our universe. The observational restriction of the reduced cosmological model is also analyzed.

In this paper, we generalized the work of Sheykhi (2011) and Ghose (2014) and establish the connection between Holographic Dark energy interacting with modified Chaplygin gas and then obtain the evolution of holographic dark energy with corresponding equation of state. In the first part of the paper, we have generalized the work of Sheykhi (2011) by choosing Hubble radius as the system’s IR cut-off and constructing the analytical form of the potentials as a function of scalar fields, namely V = V (ϕ) as well as this dynamics of the scalar fields as a function of time, namely ϕ = ϕ(t) then we have implemented the connection between Holographic dark energy and scalar fields model including quintessence, tachyon, K−essence and dilaton energy density in a (2+1)−dimensional spacetime FRW universe. In the second part of the paper, we have generalized the work of Ghose (2014) and investigate holographic dark energy (HDE) correspondence of interacting Modified Chaplygin Gas (MCG), and obtained evolution of the HDE with the corresponding equation of state. Considering the present value of the density parameter a stable configuration is found which accommodates Dark Energy (DE). We note a connection between DE and Phantom fields. It reveals that the DE might have evolved from a Phantom state in the past. We also obtained the stability of the model and analyzed the physical and geometrical interpretations of the cosmological model with reference to the (2 + 1)−dimensional spacetime.

The generalized Brans-Dicke (GBD) theory is studied in this paper. The GBD theory is obtained by generalizing the Ricci scalar R to an arbitrary function f (R) in the original Brans-Dicke (BD) action. An interesting property was found in the GBD theory, for example, it can naturally solve the problem of the $ \gamma$ value emerging in f (R) modified gravity (i.e. the inconsistent problem between the observational $ \gamma$ value and the theoretical $ \gamma$ value), without introducing the so-called chameleon mechanism. In this paper, we derive the cosmological equations and study the cosmology in the GBD theory. The cosmological solutions show that the GBD model can pass through the test of the observations, such as the observational Hubble data. Compared with other theories, it can be found that the GBD theory has some other interesting properties or solve some problems existing in other theories. 1) It is well known that the f (R) theory is equivalent to the BD theory with a potential (abbreviated as BDV) for taking a specific value of the BD parameter $ \omega$ = 0 , where the specific choice $ \omega$ = 0 for the BD parameter is quite exceptional, and it is hard to understand the corresponding absence of the kinetic term for the field. However, for the GBD theory, it is similar to the coupled scalar field model, where both fields in the GBD theory have the non-disappeared dynamical effect. 2) One knows that in the coupled scalar field quintom model, it is required to include both the canonical quintessence field and the non-canonical phantom field, in order to make the state parameter cross over w = - 1 , while several fundamental problems are associated with the phantom field, such as the problem of negative kinetic term, the fine-tuning problem, etc. On the other hand, in the GBD model, the state parameter of geometrical dark energy can cross over the phantom boundary w = - 1 as in the quintom model, without bearing the problems existing in the quintom model. 3) The GBD theory tends to investigate the physics from the viewpoint of geometry, while the BDV, or the two scalar fields quintom model tend to solve physical problems from the viewpoint of matter. It is possible that several special characteristics of scalar fields could be revealed through studies of geometrical gravity in the GBD theory. As an example, we investigate the potential V( $ \phi$ ) of the BD scalar field, and an effective form of V( $ \phi$ ) could be given by studying the GBD theory. Moreover, it seems that a viable condition for the BD theory could be found, i.e. the BD parameter should be $ \omega$ > 0 for f > 0 , if we assume that the effective form of the BD potential can be approximately written as a popular square function of $ \phi$ .

In this work, we study a new kind of dark energy (DE), which is named as “Yang—Mills condensate” (YMC). We study the stability and wde — w'de analysis of YMC DE model. Then we correspond it with quintessence, k-essence, tachyon, phantom, dilaton, DBI-essence and hessence scalar field models of DE in FRW spacetime to reconstruct potentials as well as the dynamics for these scalar fields for describing the acceleration of the universe. We also analyze the models in graphically to interpret the nature of the scalar fields and corresponding potentials.

We examine dark energy models in which a quintessence or a phantom field, $\phi$, rolls near the vicinity of a local minimum or maximum, respectively, of its potential $V(\phi)$. Under the approximation that $(1/V)(dV/d\phi) \ll 1$, [although $(1/V)(d^2 V/d\phi^2)$ can be large], we derive a general expression for the equation of state parameter $w$ as a function of the scale factor for these models. The dynamics of the field depends on the value of $(1/V)(d^2 V/d\phi^2)$ near the extremum, which describes the potential curvature. For quintessence models, when $(1/V)(d^2 V/d\phi^2)<3/4$ at the potential minimum, the equation of state parameter $w(a)$ evolves monotonically, while for $(1/V)(d^2 V/d\phi^2)>3/4$, $w(a)$ has oscillatory behavior. For phantom fields, the dividing line between these two types of behavior is at $(1/V)(d^2 V/d\phi^2) = -3/4$. Our analytical expressions agree within 1% with the exact (numerically-derived) behavior, for all of the particular cases examined, for both quintessence and phantom fields. We present observational constraints on these models.

There exist field theory models where the fermionic energy–momentum tensor contains a term proportional to [Formula: see text] which may contribute to the dark energy. We show that this new field theory effect can be achieved in the Two Measures Field Theory (TMT) in the cosmological context. TMT is an alternative gravity and matter field theory where the gravitational interaction of fermionic matter is reduced to that of General Relativity when the energy density of the fermion matter is much larger than the dark energy density. In this case also the fifth force problem is solved automatically. In the opposite limit, where the magnitudes of fermionic energy density and scalar field dark energy density become comparable, nonrelativistic fermions can participate in the cosmological expansion in a very unusual manner. Some of the features of such Cosmo-Low-Energy-Physics (CLEP) states are studied in a toy model of the late time universe filled with homogeneous scalar field and uniformly distributed nonrelativistic neutrinos, and the following results are obtained: neutrino mass increases as m ∝ a3/2 (a is the scale factor); the proportionality factor in the noncanonical contribution to the neutrino energy–momentum tensor (proportional to the metric tensor) approaches a constant as a(t) → ∞ and therefore the noncanonical contribution to the neutrino energy density dominates over the canonical one ~ m/a3 ~ a-3/2 at the late enough universe; hence the neutrino gas equation-of-state approaches w = -1, i.e. neutrinos in the CLEP regime behave as a sort of dark energy as a → ∞; the equation-of-state for the total (scalar field + neutrino) energy density and pressure also approaches w = -1 in the CLEP regime; besides the total energy density of such universe is less than it would be in the universe filled with the scalar field alone. An analytic solution is presented. A domain structure of the dark energy seems to be possible. We speculate that decays of the CLEP state neutrinos may be both an origin of cosmic rays and responsible for a late super-acceleration of the universe. In this sense the CLEP states exhibit simultaneously new physics at very low densities and for very high particle masses.

The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called $\gamma$-metric and Erez-Rosen metric with quadrupole moment $q$, influence of the additional deformation parameters $\gamma_*$ and $q_*$ generated by the scalar field is studied. It is shown that the null energy condition is satisfied for the phantom field, but it is not satisfied for the standard scalar field. The test particle motion in the both modified $\gamma$-metric and Erez-Rosen quadrupole metric is studied; the circular geodesics are determined, and near-circular trajectories are explicitly presented for characteristic values of the spacetime parameters. It is also demonstrated that the parameters $\gamma_*$ and $q_*$ have no influence on the test particle motion in the equatorial plane.

Dark energy is the constituent with an enormous abundance in the present Universe, responsible for the Universe's accelerated expansion. Therefore, it is plausible that dark energy may interact within any compact astrophysical object. The author in [S. S. Yazadjiev, Phys. Rev. D 83, 127501 (2011)] constructs an exact star solution consisting of ordinary matter and a phantom field from a constant density star (CDS) known as the Schwarzschild interior solution. The star denotes a dark energy star (DES). The author claims that the phantom field represents dark energy within the star. So far, the role of the phantom field as dark energy in a DES is not systematically studied yet. Related to this issue, we analyze the energy condition of a DES. We expect that DESs shall violate the strong energy condition (SEC) for a particular condition. We discover that a SEC is fully violated only when the compactness reaches the Buchdahl limit. Furthermore, we also investigate the causal conditions and stabilities due to the convective motion and gravitational cracking. We also find that those conditions are violated. These results indicate that DES is not physically stable. However, we may consider DES as an ultracompact object of which we can calculate the gravitational wave echo time and echo frequency and compare them to those of CDS. We find that the contribution of the phantom field delays the gravitational wave echoes. The effective potential of the perturbed DES is also studied. The potential also enjoys a potential well like CDS but with a deeper well. We also investigate the possibility that DES could form a gravastar when $C=1$. It is found that a gravastar produced from DES possesses no singularity with a dS-like phase as the interior. These results could open more opportunities for the observational study of dark energy in the near future, mostly from the compact astrophysical objects.