A cosmological exact solution of generalized Brans-Dicke theory with complex scalar field and its phenomenological implications

When the Brans-Dicke theory is formulated in terms of the Jordan scalar field φ, the amount of dark energy is related to the mass of this field. We investigate a solution which is relevant to the late universe. We show that if φ is taken to be a complex scalar field, then an exact solution to the vacuum equations requires that the Friedmann equation possesses both a constant term and one which is proportional to the inverse sixth power of the scale factor. Possible interpretations and phenomenological implications of this result are discussed.     

Analysis of an FRW cosmological model

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.      

Cosmological Model Based on Gauge Theory of Gravity

A cosmological model based on gauge theory of gravity is proposed in this paper. Combining cosmological principle and field equation of gravitational gauge field, dynamical equations of the scale factor R(t) of our universe can be obtained. This set of equations has three different solutions. A prediction of the present model is that, if the energy density of the universe is not zero and the universe is expanding, the universe must be space-flat, the total energy density must be the critical density ρ_c of the universe. For space-flat case, this model gives the same solution as that of the Friedmann model. In other words, though they have different dynamics of gravitational interactions, general relativity and gauge theory of gravity give the same cosmological model.     

A Non-Singular Universe with Vacuum Energy

A model for the universe based on the back-reaction effects of quantum fields at finite temperature in the background of Robertson-Walker spacetime and in the presence of a non-zero cosmological constant is constructed. We discuss the vacuum regime in the light of the results obtained through previous studies of the back-reaction of massless quantum fields in the static Einstein universe, and we argue that an adiabatic vacuum state and thermal equilibrium is achieved throughout this regime. Critical density is maintained naturally from the very early stages as a consequence of back-reaction effect of the vacuum fluctuations of quantum fields. Results show that such a model can explain many features of the early universe as well as the present universe. The model is free from the basic problems of the standard Friedmann cosmology, and is non-singular but involves a continuous creation of energy at a rate proportional to the size of the universe, which is lower than that suggested by the steady-state cosmology.     

量子纠缠与宇宙学弗里德曼方程

量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球（a geodesic ball）的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.     

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.     

离散时空的Friedmann宇宙的几何结构及其性质

研究了离散时空的Friedmann宇宙的几何结构,证明了形成Friedmann宇宙的尘埃物质并不分布在Friedmann时空点上,导出了在Friedmann宇宙中的试验粒子的测地运动方程,并揭示了Friedmann宇宙中的时钟和频移效应. 关键词： Friedmann时空 尘埃物质 测地运动 时频效应     

Brane-Cosmology Dynamics with Induced Gravity

The Friedmann equations for a brane with induced gravity are analyzed and compared with the standard general relativity and Randall-Sundrum cases. Randall-Sundrum gravity modifies the early universe dynamics, whereas induced gravity changes the late universe evolution. The early and late time limits are investigated. Induced gravity effects can contribute to late-universe acceleration. The conditions for this are found. Qualitative analysis is given for a range of scalar field potentials.     

Thermodynamics of apparent horizon and modified Friedmann equations

Starting from the first law of thermodynamics, dE=T _h ? dS _h +W? dV, at the apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a quantum-corrected relation, $S=\frac{A}{4G}-\alpha \ln \frac{A}{4G}+\beta \frac{4G}{A}$ , we derive modified Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy including the quantum-corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon. Our study shows that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.     

Exothermic Transition to a Future Susy Universe

The Higgs sector of the MSSM may be extended to solve the μ problem by the addition of a gauge singlet scalar field. We consider an extended Higgs model. For simplicity we consider the case where all the fields in the scalar sector are real. We analyze the vacuum structure of the model. We address the question of an exothermic phase transition from a broken susy phase with electroweak symmetry breaking (our current universe) to an exact susy phase with electroweak symmetry breaking (future susy universe).     

New classes of exact solutions in inflationary cosmology

The problem of determining a representation of the self-interaction potential in the form of a time dependence of the field potential energy which admits the existence of an inflationary regime and the transition of evolution to a Friedmann regime of asymptotic expansion is investigated within a cosmological model with a self-interacting scalar field. A variational formulation of the slow-roll concept is introduced, and, on the basis thereof, an exact solution is constructed for the evolution of the scale factor and the form of the self-interaction potential. A method based on representing the Einstein equations in the form of a linear second-order equation is developed for constructing and analyzing exact cosmological solutions of these equations. Selected types of potentials and the corresponding evolutions of the universe are investigated. Zh. éksp. Teor. Fiz. 114, 406–417 (August 1998)     

Quantum vacuum cosmology

It is shown for the case of a conformally flat vacuum that the curvature of space-time may be viewed as the observable consequence of particle interactions involving a scalar field φ, rather than the independent agency of the gravitational field by itself. The quantum nature of gravity comes in as a consequence of the quantum properties of the φ-field (“vacuum fluctuation”), and a direct analogy is drawn between the renormalizations of charge and mass. Cosmological solutions are derived: These being just the conventional Friedmann solutions, or the de Sitter solution. It is pointed out that a totally empty universe must be Minkowskian.     

Magnetic fields and the Weyl tensor in the early universe

We have solved the Einstein–Maxwell equations for a class of metrics with constant spatial curvature by considering only a primordial magnetic field as source. We assume a slight modification of the Tolman averaging relations so that the energy–momentum tensor of this field possesses an anisotropic pressure component. This inhomogeneous magnetic universe is isotropic and its time evolution is guided by the usual Friedmann equations. In the case of a flat universe, the space-time metric is free of singularities (except the well-known initial singularity at \(\text {t} = 0\) ). It is shown that the anisotropic pressure of our model has a straightforward relation to the Weyl tensor. We then analyze the effect of this new ingredient on the motion of test particles and on the geodesic deviation of the cosmic fluid.     

Cosmological inflation models admitting natural emergence to the radiation-dominated stage and the matter domination era

A model of the evolution of the uniform and isotropic spatially-flat universe, where the inflation stage emerges naturally into the radiation-dominated stage and the matter-dominated era, is proposed on the basis of exact solutions of the self-consistent equations of a gravitating self-acting scalar field. It is shown that the model contains two basic physical mechanisms, one of which is related with the decay of Higgs bosons and provides for the inflation stage, while the second mechanism is associated with the adiabatic expansion of the universe filled with matter with a definite equation of state and gives a Friedmann expansion regime.     

Stochastic evolution of cosmological parameters in the early universe

We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early universe. We consider the stochastic evolution of density parameter in the early universe after the inflationary phase qualitatively, under the assumption of fluctuating w factor in the equation of state, in the Fokker-Planck formalism. Since the scale factor for the universe depends on the energy density, from the coupled Friedmann equations we calculated the two variable probability distribution function assuming a flat space geometry.     

Particle creation in a f(R) theory with cosmological constraints

The novel idea that spatial expansion of our universe can be regarded as the consequence of the emergence of space was proposed by Padmanabhan. By using of the basic law governing the emergence, which Padmanabhan called holographic equipartition, he also arrives at the Friedmann equation in a flat universe. When generalized to other gravity theories, the holographic equipartition need to be generalized with an expression of $f(\Delta N,N_{sur})$ . In this paper, we give general expressions of $f(\Delta N,N_{sur})$ for generalized holographic equipartition which can be used to derive the Friedmann equations of the Friedmann–Robertson–Walker universe with any spatial curvature in higher ( $\hbox {n}+1$ )-dimensional Einstein gravity, Gauss–Bonnet gravity and more general Lovelock gravity. The results support the viability of the perspective of holographic equipartition.     

Constraints from Type Ia supernovae on the Λ-CDM model in Randers-Finsler space

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann equation and a new luminosity distance-redshift relation is proposed. A best-fit to the Type Ia supernovae (SNe) observations yields that the Ω_Λ in the Λ-CDM model is suppressed to almost zero. This fact indicates that the astronomical observations on the Type Ia SNe can be described well without invoking any form of dark energy. The best-fit age of the universe is given. It is in agreement with the age of our galaxy.     

The creation of particles from a vacuum in a nonsteady isotropic universe

The paper considers the creation of particles from a vacuum in a closed, open, and quasi-Euclidean Friedmann model. Finite general expressions are obtained for the density of the number of pairs created, and also new analytical estimates are given of the intensity of processes of creation at different stages of evolution of the universe.     

Spatially-Hyperbolic Friedmann–Robertson–Walker Universe with Potentially Broken Z2−Symmetry

For the Friedmann–Robertson–Walker (FRW) Universe with negative curvature, sustained by a spontaneous Z₂? symmetry breaking scalar field, depending on time alone, we have derived the Einstein–Gordon system of equations. For physically relevant cases, the matter-curvature system have been numerically analyzed.     

Remarks on the Idea of Spontaneous Break-Down of Symmetry,Cosmic Variability of Eddington's Number,Mach's Idea Concering the Origin of Inertia,and Field Equations Describing Global and Local Gravitational Fields

Subject is considered on the level of classical field theory. We start from some aspects of the theory of ferromagnets. Their counterpart in classical field theory is pointed out using the over simplified model of a selfinteracting scalar field. The ground state (“vacuum expection value”) of the scalar field is interpreted as cosmic background field, which can be considered as constant for local physical phenomena. In practice, however, it is a function of the age of universe. Which kind of function it could be is suggested by a discussion of the cosmic variability of Eddington's number γ = 10⁴⁰, which refers to Dirac's consideration of this problem. But contrary to Dirac's assumption that atomic quantities are constant, we suppose that the inertial mass of elementary particles is a function of the age of universe. The cosmic gravitational field is described by other equations than the gravitational field created by local matter distributions. The field equations for the local gravitational field we start from reduce to Einstein's equations, if we neglect the possible influence of the universe on local phenomena. In case that the cosmic matter is homogeneously and isotropically distributed, the field equations for the cosmic gravitational field permit only such a time dependent solution the three-spaces of which are linearly expanding and spherically closed. The different field equations for cosmic and local gravitational fields are considered approximations of more fundamental field equations which approximately split into two sets of equations, if it is possible to contrast local physical systems with the universe. The described cosmological model taken as a basis, the inertial mass of elementary particles becomes a function of the matter density creating the cosmic gravitational field. This could be considered as, at least, partly realisation of Mach's idea concerning the origin of inertia. Starting from the interpretation of the ground state (vacuum expection value) as a function of a certain cosmic background field, more realistic gage field models could give the following picture of cosmic development: In the far past there was a state of the universe characterized by enormous contraction of matter. In this stage of development, it was impossible to contrast particles with the universe. Matter expands and it becomes possible to contrast certain physical systems with the universe. But the ground state is such a symmetric one that only fields with vanishing rest mass can be contrasted with the universe (ferromagnet above Curie temperature). With further expansion of the universe the ground state will lose certain symmetry properties. By this it becomes possible that you get the impression there are particles with nonvanishing rest mass (ferromagnet below Curie temperature). Finally, the influence of the universe on local physical systems goes to zero with further expansion. Especially, this means the inertial mass of elementary particles goes to zero, too (Curie temperature of ferromagnetic material goes to zero with cosmic expansion).