The conformal status of o = ‐3/2 Brans‐Dicke cosmology

Following recent fit of supernovae data to Brans‐Dicke theory which favours the model with o = ‐ 3/2 [1] we discuss the status of this special case of Brans‐Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit o = ‐3/2 is consistent only with the vacuum field equations and it makes such a Brans‐Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans‐Dicke theory with o = ‐3/2 gives a border between a standard scalar field model and a ghost/phantom model. In this paper we show that in o = ‐3/2 Brans‐Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non‐zero spatial curvature except for k=‐1 case. Further we show that this k=‐1 case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non‐zero spatial curvature models of Kantowski‐Sachs type are admissible in o = ‐3/2 Brans‐Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.     

An interacting scalar field and the recent cosmic acceleration

In this paper it is shown that the Brans – Dicke scalar field itself can serve the purpose of providing an early deceleration and a late time acceleration of the universe without any need of quintessence field if one considers an interaction, i.e., transfer of energy between the dark matter and the Brans – Dicke scalar field.     

Exact Kantowski-Sachs Anisotropic Dark Energy Cosmological Models in Brans Dicke Theory of Gravitation

The main purpose of this paper is to explore the solution of Exact Kantowski-Sach cosmological models by using the Brans Dicke Theory of gravitation in the background of anisotropic dark energy. In order to obtain different physically variable models of the universe we have assumed the special law of variation of Hubbles parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) which yields constant deceleration parameter and power law relation between average scale factor R and scalar field f, which has already been used by Johri and Desikan in RW Brans Dicke models. Some physical and geometrical consequences of the models have been carried out by using some physical quantities.     

A Class of Renormalization Group Invariant Scalar Field Cosmologies

We present a class of scalar field cosmologies with a dynamically evolving Newton parameter G and cosmological term . In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for G and near a fixed point. Moreover, we propose a modified action for gravity which includes the effective running of G and near the fixed point. A proper understanding of the associated variational problem is obtained upon considering the four-dimensional gradient of the Newton parameter.     

Anisotropic string cosmological model in Brans–Dicke theory of gravitation with time-dependent deceleration parameter

We discuss a spatially homogeneous and anisotropic string cosmological models in the Brans–Dicke theory of gravitation. For a spatially homogeneous metric, it is assumed that the expansion scalar θ is proportional to the shear scalar σ. This condition leads to A = kB^m, where k and m are constants. With these assumptions and also assuming a variable scale factor a = a(t), we find solutions of the Brans–Dicke field equations. Various phenomena like the Big Bang, expanding universe, and shift from anisotropy to isotropy are observed in the model. It can also be seen that in early stage of the evolution of the universe, strings dominate over particles, whereas the universe is dominated by massive strings at the late time. Some physical and geometrical behaviors of the models are also discussed and observed to be in good agreement with the recent observations of SNe la supernovae.     

Whitrow-Randall's relation and Brans-Dicke cosmology

When Brans and Dicke published their alternative gravitational framework, they proved that it led to Machian solutions in the static case, and for a pressureless (dust) Euclidean universe. We extend their demonstration to Euclidean and non-Euclidean models with non-null pressure, employing the perfect fluid model. We find andp both G.     

Bianchi Type-II, VIII & IX Cosmological Models with Strange Quark Matter Attached to String Cloud in Brans–Dicke and General Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi type-II, VIII & IX cosmological models with strange quark matter attached to string cloud in Brans and Dicke (Phys. Rev. C 71:054905, 1961) scalar tensor theory and general theory of gravitation. Some important features of the models, thus obtained, have been discussed. We noticed that these universes always expand isotropically and the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

Plane-Symmetric Solitons of Spinor and Scalar Fields

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms S= and P=i⁵; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant = _,^,, that becomes linear at 0. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations have been obtained. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered.     

Orbiting naked singularities in large-$$\omega $$ Brans–Dicke gravity

Brans–Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)–tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the \(\omega \longrightarrow \infty \) limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar–tensor gravity.     

Euclidean non-vacuum wormholes in Brans－Dicke theory

The Brans－Dicke theory is investigated in which the Pauli metric is identified to be a physical spacetime metric. The solutions of a wormhole are obtained in Brans－Dicke theory with a relativistic radiation field for ω>-3/2. However, it is found that one cannot construct a wormhole in the presence of a 3-form axion field.     

Bianchi type-I,V and VIo models in modified generalized scalar-tensor theory

In modified generalized scalar-tensor (GST) theory, the cosmological term Λ is a function of the scalar field ϕ and its derivatives . We obtain exact solutions of the field equations in Bianchi Type-I, V and VIo space-times. The evolution of the scale factor, the scalar field and the cosmological term has been discussed. The Bianchi Type-I model has been discussed in detail. Further, Bianchi Type-V and VIo models can be studied on the lines similar to Bianchi Type-I model.      

On Spherically Symmetric Minimally Coupled Brane Worlds

For a static, spherically symmetric brane in the framework of the RS2 concept, we study the conditions under which the 4D tensor E _v, arising from the 5D Weyl tensor, vanishes on the brane. Gravity on the brane is then decoupled from the bulk geometry, it is the so-called minimally coupled brane world (MCBW). Assuming E _v =0 in the whole bulk, we try to solve the 5D Einstein equations G _AB + _5gAB =0 and obtain an overdetermined set of equations for functions of the radial coordinate. Some special solutions are found, among which are the well-known black string solution with the Schwarzschild metric on the brane and its generalizations with Schwarzschild–(A)dS on-brane metrics. It is concluded that a MCBW can be embedded, in general, in a bulk where E_v is not identically zero but only vanishes on the brane. We also present some previous results on the general properties of scalar fields on the brane and give an example of a wormhole supported by a scalar field in a MCBW.     

Bianchi Types II, VIII and IX String Cosmological Models with Bulk Viscosity in Brans-Dicke Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi types II, VIII and IX string cosmological models with bulk viscosity in a scalar tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). It is observed that in case of Bianchi type-IX universe, only bulk viscous cosmological model exists. Some physical and geometrical properties of the models are also discussed.     

Correlation inequalities for a class of even ferromagnets

We present rigorous correlation inequalities for connectedn-point functions in a class of even ferromagnets. The class includes spin-1/2 Ising models and scalar field models with potential functionV which is even and continuously differentiable withV convex on [0, ). These inequalities are obtained by pushing ahead with the method of Ellis, Monroe, and Newman at its maximum.     

Dynamical system approach to scalar–vector–tensor cosmology

Using scalar–vector–tensor Brans Dicke (VBD) gravity (Ghaffarnejad in Gen Relativ Gravit 40:2229, 2008; Gen Relativ Gravit 41:2941, 2009) in presence of self interaction BD potential \(V(\phi )\) and perfect fluid matter field action we solve corresponding field equations via dynamical system approach for flat Friedmann Robertson Walker metric (FRW). We obtained three type critical points for \(\Lambda CDM\) vacuum de Sitter era where stability of our solutions are depended to choose particular values of BD parameter \(\omega \). One of these fixed points is supported by a constant potential which is stable for \(\omega <0\) and behaves as saddle (quasi stable) for \(\omega \ge 0\). Two other ones are supported by a linear potential \(V(\phi )\sim \phi \) which one of them is stable for \(\omega =0.27647\). For a fixed value of \(\omega \) there is at least 2 out of 3 critical points reaching to a unique critical point. Namely for \(\omega =-0.16856(-0.56038)\) the second (third) critical point become unique with the first critical point. In dust and radiation eras we obtained one critical point which never become unique fixed point. In the latter case coordinates of fixed points are also depended to \(\omega \). To determine stability of our solutions we calculate eigenvalues of Jacobi matrix of 4D phase space dynamical field equations for de Sitter, dust and radiation eras. We should point also potentials which support dust and radiation eras must be similar to \(V(\phi )\sim \phi ^{-\frac{1}{2}}\) and \(V(\phi )\sim \phi ^{-1}\) respectively. In short our study predicts that radiation and dust eras of our VBD–FRW cosmology transmit to stable de Sitter state via non-constant potential (effective variable cosmological parameter) by choosing \(\omega =0.27647\).     

The infinite atom Dicke maser model II

We study the time evolution of a quantum field under a Hamiltonian constructed in an earlier paper by taking the limits asn of a Dicke maser model Hamiltonian forn radiating atoms. We show that the radiation field converges to a dynamic equilibrium state independent of its initial state and that the strength of the field is inversely proportional to the square of the distance from the source. A number of variations of the Hamiltonian are also considered.     

Rigorous Estimates of the Tails of the Probability Distribution Function for the Random Linear Shear Model

In previous work Majda and McLaughlin, and Majda computed explicit expressions for the 2Nth moments of a passive scalar advected by a linear shear flow in the form of an integral over R ^N . In this paper we first compute the asymptotics of these moments for large moment number. We are able to use this information about the large-N behavior of the moments, along with some basic facts about entire functions of finite order, to compute the asymptotics of the tails of the probability distribution function. We find that the probability distribution has Gaussian tails when the energy is concentrated in the largest scales. As the initial energy is moved to smaller and smaller scales we find that the tails of the distribution grow longer, and the distribution moves smoothly from Gaussian through exponential and stretched exponential. We also show that the derivatives of the scalar are increasingly intermittent, in agreement with experimental observations, and relate the exponents of the scalar derivative to the exponents of the scalar.     

Letter: The Real Scalar Field in Schwarzschild-de Sitter Spacetime

In this paper, the real scalar field equation in Schwarzschild-de Sitter spacetime is solved numerically with high precision. A method called polynomial approximation is introduced to derive the relation between the tortoise coordinate x and the radius r. This method is different from the tangent approximation [1] and leads to more accurate results. The Nariai black hole is then discussed in details. We find that the wave function is harmonic only near the horizons as I. Brevik and B. Simonsen [1] found. However the wave function is not harmonic in the region of the potential peak, with amplitude increasing instead. Furthermore, we also find that, when the cosmological constant decreases, the potential peak increases, and the maximum wave amplitude increases.     

The role of a vector-valued field in multidimensional universe geometry

For a model of the multidimensional universe we take a smooth manifold S which under the action of a compact Lie group G fibres into orbits of the same type G/H acquiring the structure of a fibre bundle with typical fibre G/H and base-the orbit space S/G (identified with the four-dimensional spacetime). The notion of a connection form on the fibre bundle SS/G is defined and its role for some geometrical structures on S is considered. In the framework of a theory of G-invariant tensor-type fields on S, it is shown that -being itself a field of this type-determines a dimensional reduction of the objects on S to objects on S/G.     

Scalar–vector–tensor gravity from preferred reference frame effects

Using some suitable combinations of a dynamical unit time-like four-velocity of a preferred reference frame, Ricci tensor and covariant derivatives of the Brans–Dicke (BD) scalar field, we propose a new scalar–vector–tensor gravity model in which an Euclidean Jordan–Brans–Dicke (JBD) action is reduced to its Lorentzian version with no used complex coordinates. Thus it should be play an important role in the process of metric signature transition of a suitable dynamical curved space-time. In this work we follow the ideas proposed by Barbero et al. As an application of the model, we study a classical perfect fluid cosmological universe described in a flat Robertson–Walker background metric. Mathematical derivations of the equations predict a non-singular scale factor for the space-time in the both of dust and radiation dominated states where value of the Brans–Dicke parameter is fixed, but there is still an arbitrary parameter which should be determined by the boundary values of the cosmological system. Furthermore its classical cosmological vacuum solutions is obtained as a non-singular model with a fixed Brans–Dicke parameter. Although there is obtained a singular perfect fluid cosmological solution which may not be suitable, because in this case the Brans–Dicke parameter is not still fixed.