Thawingf(R)cosmology

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.

Exact solutions of Bianchi type-II cosmological models with stiff matter are obtained in the Brans-Dicke scalar tensor theory and the behaviour of the models is discussed.

We discuss wormhole solution in the Brans-Dicke theory with existence of relativistic radiation field. The solutions of wormhole are obtained in the Einstein frame. When the dilaton field σ = const, the solution of wormhole should be reduced to the well-known Tolman wormhole. Euclidean wormhole solution also has been obtained in the Einstein frame when σ ≠ const. For the comparison, we also derive the wormhole solution in the Jordan frame with existence of relativistic radiation field. However, the two frames, the Einstein frame and the Jordan frame, are not physically equivalent.

Vacuum solutions of the field equations that satisfy the original notion of the plane wave, namely gμν=gμν(Z), Z=Σμaμxμ, aμ’s being constants and gμνZ,μZ,ν=0, are sought for both Brans–Dicke scalar–tensor theory and the more recent scalar–tensor theory due to Sen and Dunn. (Here Greek letters range from 1 to 4 and Latin letters from 1 to 3.) A complete set of solutions are obtained for both cases. Although not required at the outset, it turns out that, in both cases, the scalar field is also function of Z alone. As a by-product, one gets the complete set of solutions of the Einstein–Maxwell equations for the null electromagnetic field for the cases when gμν satisfies the above-mentioned requirement.

The duality between a higher-curvature f(R) gravity model and a scalar-tensor theory helps to bring out the role of the additional degree of freedom originating from the higher-derivative terms in the gravity action. Such a degree of freedom which appears as a scalar field has been shown to have multiple implications in the cosmological/astrophysical scenario. The present work proposes a novel generalization to this correspondence between f(R) gravity and a dual scalar-tensor theory when the affine connection is considered to have an antisymmetric part. It turns out that the f(R) action in the presence of spacetime torsion can be recast to a coupled scalar-tensor theory with a 2-rank massless antisymmetric tensor field in the Einstein frame, where the scalar field gets coupled with the antisymmetric field through derivative coupling(s).

We study charged boson stars in scalar-tensor (ST) gravitational theories. We analyze the weak field limit of the solutions and analytically show that there is a maximum charge to mass ratio for the bosons above which the weak field solutions are not stable. This charge limit can be greater than the GR limit for a wide class of ST theories. We numerically investigate strong field solutions in both the Brans-Dicke and power law ST theories. We find that the charge limit decreases with increasing central boson density. We discuss the gravitational evolution of charged and uncharged boson stars in a cosmological setting and show how, at any point in its evolution, the physical properties of the star may be calculated by a rescaling of a solution whose asymptotic value of the scalar field is equal to its initial asymptotic value. We focus on evolution in which the particle number of the star is conserved and we find that the energy and central density of the star decrease as the cosmological time increases. We also analyze the appearance of the scalarization phenomenon recently discovered for neutron stars configurations and, finally, we give a short discussion on how making the correct choice of mass influences the argument over which conformal frame, the Einstein frame or the Jordan frame, is physical.

Comparing scalar–tensor gravity and [formula omitted]-gravity in the Newtonian limit

The dynamics of the Brans-Dicke (BD) cosmology in the Einstein frame is studied. We implement phase-space analysis in order to investigate the role of initial conditions and model parameters in the evolution of the universe. The phase plane algorithm and stability of the model are considered in the Einstein Frame where the cosmological background is described in Λ-Cold Dark Matter (ΛCDM) and is supplemented by a Jordan-Fierz-Brans-Dicke field. Our results show: (1) The model parameter α (the coupling strength of the BD scalar field to matter sources) in the Einstein frame plays an important role in the model stability whereas the initial conditions significantly affect the cosmic dynamics. (2) Using type Ia SNIa data, we fit the parameters of the model with observation and show that the current value of the effective equation of state (EoS) parameter is within the range supported by observations. (3) The phase space analysis implies that the universe approaches an attractor in the near future.

Invariance of the Brans-Dicke scalar-tensor theory of gravity under scale transformations of the second kind is discussed. It is shown that the requirement of scale invariance of the second kind leads to the unique value −32 of the adjustable parameter ω in the Brans-Dicke theory. It is further shown that, in order to obtain a consistent set of equations, matter must be coupled to the scalar-tensor field in such a way that the whole theory can be transformed into the usual Einstein tensor theory. This is accomplished by performing a space-time dependent scale change such that the transformed scalar field is everywhere a constant.

Objectives: To derive the multi-fluid anisotropic Bianchi type-III cosmological model filled with radiation and matter in the presence of Brans-Dicke scalar-tensor theory. Method: In this paper, we have calculated Brans-Dicke field equations in anisotropic Bianchi type -III space times in the presence of matter and radiation which are minimally interacting fields. To obtain the determinate solution of the model, we considered i) the state of the equation , ii) the shear scalar is directly proportional to the expansion scalar i.e., . Also, consider the deceleration parameter, , where with which yields models with constant deceleration parameter. Findings: This solution shows an anisotropic radiation model in Brans-Dicke's theory. Also, it shows accelerated expansion of the universe and transition of the universe from the deceleration phase to the accelerated phase. Novelty: The derived model's many parameters support recent cosmological findings, indicating the model's good discovery. Thus, within the framework of our established model, we are able to comprehend the cosmic development. Keywords: Bianchi type-III, Brans-Dicke theory, Multifluid, Deceleration parameter, Λ CDM

The gravitational wave equation for a spatially flat Friedmann-Robertson-Walker universe is derived in the context of scalar-tensor theories of gravity, which have the Brans-Dicke theory as a particular case. This equation is solved for several cosmological scenarios, including the expansions governed by the Nariai as well as the Gurevich-Finkelstein-Ruban solutions of Brans-Dicke theory and for a new set of exact solutions of other scalar-tensor theories. The amplification of gravitational waves is studied in comparison to what happens in the general relativistic case. It is shown how the coupling with the scalar field changes the scales defining very large and very small wave numbers, and consequently the value of the amplification coefficient. It is found that very small values for the coupling parameter could lead to amplification of subhorizon waves. The creation of the corresponding high-frequency gravitons is explained as a response to the rapid time variation of the gravitational "constant," which can occur near the singularity in some models. It is also shown that there could be amplification of waves even in a radiation-dominated universe in some cases, because the wave equation is not conformally invariant, except for the case of Nariai's solution in the Brans-Dicke theory.

Holographic dark energy

The conformal transformations presented in the previous chapter establish a mathematical equivalence between scalar-tensor theories and Einstein’s general relativity, with the modifications dictated by the anomalous coupling of the Einstein frame scalar to ordinary matter and its consequences. A priori, the mathematical equivalence need not be a physical one. The literature using conformal transformations in cosmology and in alternative theories of gravity is plagued by confusion and ambiguity on the issue of the physical equivalence of the two conformal frames, or which frame should be regarded as the physical one. As a consequence, the conformal transformation technique is often misused and its results are given erroneous interpretations. Incompatible points of view occurring in the literature support the following ideas [613, 363] : (first viewpoint) that the Jordan and the Einstein frame are physically equivalent, (second viewpoint) that the two frames are inequivalent the Jordan frame is the physical one, and the Einstein frame is unphysical, (third viewpoint) that the two frames are inequivalent — the Jordan frame is unphysical, and the Einstein frame is physical.

We find a black hole solution with non-Abelian field in Brans-Dicke theory.\nIt is an extension of non-Abelian black hole in general relativity. We discuss\ntwo non-Abelian fields: "SU(2)" Yang-Mills field with a mass (Proca field) and\nthe SU(2)$\\times$SU(2) Skyrme field. In both cases, as in general relativity,\nthere are two branches of solutions, i.e., two black hole solutions with the\nsame horizon radius. Masses of both black holes are always smaller than those\nin general relativity. A cusp structure in the mass-horizon radius\n($M_{g}$-$r_{h}$) diagram, which is a typical symptom of stability change in\ncatastrophe theory, does not appear in the Brans-Dicke frame but is found in\nthe Einstein conformal frame. This suggests that catastrophe theory may be\nsimply applied for a stability analysis as it is if we use the variables in the\nEinstein frame. We also discuss the effects of the Brans-Dicke scalar field on\nblack hole structure.\n

Scalar–tensor gravitation theories, such as the Brans–Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry–Émery–Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the ‘Jordan frame’. Just as, in General Relativity, natural energy conditions on the stress–energy tensor become conditions on the Ricci tensor, in scalar–tensor theories expressed in the Jordan frame natural energy conditions become conditions on the Bakry–Émery–Ricci tensor. We show that, if the Bakry–Émery tensor obeys the null energy condition with an upper bound on the Bakry–Émery scalar function, there is a modified notion of apparent horizon which obeys analogues of familiar theorems from General Relativity. The Bakry–Émery modified apparent horizon always lies behind an event horizon and the event horizon obeys a modified area theorem. Under more restrictive conditions, the modified apparent horizon obeys an analogue of the Hawking topology theorem in four spacetime dimensions. Since topological censorship is known to yield a horizon topology theorem independent of the Hawking theorem, in an appendix we obtain a Bakry–Émery version of the topological censorship theorem. We apply our results to the Brans–Dicke theory, and obtain an area theorem for horizons in that theory. Our theorems can be used to understand behaviour observed in numerical simulations by Scheel et al (1995 Phys. Rev. D 51 4236–49) of dust collapse in Brans–Dicke theory.