Repulsive gravity induced by a conformally coupled scalar field implies a bouncing radiation-dominated universe

In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity (Novello in Phys Lett 90A:347 1980). When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such broken symmetry state.     

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992, E.E. Podkletnov and R. Nieminen found that under certain conditions, ceramic superconductor with composite structure reveals weak shielding properties against gravitational force. In classical Newton's theory of gravity and even in Einstein's general theory of gravity, there are no grounds of gravitational shielding effects. But in quantum gauge theory of gravity, the gravitational shielding effects can be explained in a simple and natural way. In quantum gauge theory of gravity, gravitational gauge interactions of complex scalar field can be formulated based on gauge principle. After spontaneous symmetry breaking, if the vacuum of the complex scalar field is not stable and uniform, there will be a mass term of gravitational gauge field. When gravitational gauge field propagates in this unstable vacuum of the complex scalar field, it will decays exponentially, which is the nature of gravitational shielding effects. The mechanism of gravitational shielding effects is studied in this paper, and some main properties of gravitational shielding effects are discussed.     

Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.     

Modified gravity inspired DGP brane cosmology

We consider a DGP brane scenario where a scalar field is present on the brane through the introduction of a scalar potential, itself motivated by the notion of modified gravity. This theory predicts that the mass appearing in the gravitational potential is modified by the addition of the mass of the scalar field. The cosmological implications that such a scenario entails are examined and shown to be consistent with a universe expanding with power-law acceleration.     

Gravitational energy in Brans-Dicke cosmological models

The behaviour of gravitational energy and scalar field during the evolution of the universe within the framework of Brans-Dicke theory has been discussed. With help of the Landau-Lifshitz pseudo-tensor for the flat Friedmann-Robertson-Walker model, it is found that (i) the total energy of the universe is always zero, (ii) the Brans-Dicke scalar field for all Ω >-0 contributes energy to the negative energy of gravitational field and this gets transferred to the vacuum energy which accelerates the expansion of the universe.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

The Redshift Periodicity of Galaxies as a Probe of the Correctness of General Relativity

Recent theoretical work determines the correct coupling constant of a scalar field to the Ricci curvature of spacetime in general relativity. The periodicity in the redshift distribution of galaxies observed by Broadhurst et al., if genuine, determines the coupling constant in the proposed scalar field models. As a result, these observations contain important information on the problem of whether general relativity is the correct theory of gravity in the region of the universe at redshifts z < 0.5.     

One-loop effective action for non-local modified Gauss–Bonnet gravity in de Sitter space

We discuss the classical and quantum properties of non-local modified Gauss–Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss–Bonnet gravity with a scalar potential. A classical, multiple de Sitter universe solution is found where one of the de Sitter phases corresponds to the primordial inflationary epoch, while the other de Sitter space solution—the one with the smallest Hubble rate—describes the late-time acceleration of our universe. A Chameleon scenario for the theory under investigation is developed, and it is successfully used to show that the theory complies with gravitational tests. An explicit expression for the one-loop effective action for this non-local modified Gauss–Bonnet gravity in the de Sitter space is obtained. It is argued that this effective action might be an important step towards the solution of the cosmological constant problem.     

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.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field φ plays in Brans–Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans–Dicke theory, we propose a new gravity theory with a complex scalar field ϕ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.     

An alternative f(R, T) gravity theory and the dark energy problem

Recently, a generalized gravity theory was proposed by Harko et al. where the Lagrangian density is an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T, known as F(R,T) gravity. In their derivation of the field equations, they have not considered conservation of the stress-energy tensor. In the present work, we have shown that a part of the arbitrary function f(R,T) can be determined if we take into account of the conservation of stress-energy tensor, although the form of the field equations remain similar. For homogeneous and isotropic model of the universe the field equations are solved and corresponding cosmological aspects has been discussed. Finally, we have studied the energy conditions in this modified gravity theory both generally and a particular case of perfect fluid with constant equation of state.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

New developments in the theory of gravity interacting with quantized fields

Renormalization in the theory of a quantized scalar field interacting with the classical Einstein gravitational field is discussed. The scalar field obeys the generalization of the Klein-Gordon equation which is conformally invariant in the limit of vanishing mass. A generalized Kasner metric corresponding to an anisotropic expansion of the universe is considered. Results obtained in collaboration with S.A. Fulling and B.L. Hu are described, which show explicitly how the infinities appearing in the expectation value of the energy-momentum tensor can be absorbed through renormalization of the cosmological constant and the coefficients of a quadratic tensor appearing in a slightly generalized form of the Einstein equation. There is also a finite renormalization of the gravitational constant.     

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).     

Gravitational Scalar-Driving Inflation Ⅱ

In the given scalar-tensor theory of gravity, the gravitational scalar ф plays the role of inflaton field, the cosmological function λ(ф) together with the coupling function ω(ф) provides a double-well potential for the motion of ф. After inflation, the universe expands according to 2/3 power law different from the Friedmann cosmology. There is no reheating and there is no need of reheating. The model predicts consistency between the Jeans mass and the mass of galaxies.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Gravitational radiation in quantum gravity

The effective field theory of quantum gravity generically predicts non-locality to be present in the effective action, which results from the low-energy propagation of gravitons and massless matter. Working to second order in gravitational curvature, we reconsider the effects of quantum gravity on the gravitational radiation emitted from a binary system. In particular, we calculate for the first time the leading order quantum gravitational correction to the classical quadrupole radiation formula which appears at second order in Newton’s constant.     

Emergent Universe in Einstein-Gauss-Bonnet Theory

In this work, Emergent Universe scenario has been developed in Einstein-Gauss-Bonnet (EGB) theory. The universe is chosen as homogeneous and isotropic FRW model and the matter in the universe has two components—the first one is a perfect fluid with barotropic equation of state p=ω ρ (ω, a constant) and the other component is a real or phantom (or tachyonic) scalar field. Various possibilities for the existence of emergent scenario has been discussed and the results are compared with those in Einstein gravity.     

Gauge-Invariant and Gauge-Fixing Independent Effective Action in One-Loop Quantum Gravity

The one-parameter dependent family of the gauge invariant and gauge fixing independent effective actions is considered in one-loop approximation. The one-loop unique effective action (chosing as the representative of this family) in d = 4 Einstein quantum gravity with scalar field and Brans-Dicke quantum theory in flat space, in d = 4 Einstein gravity on De Sitter background, in higher derivative gravity on d-dimensional torus compactified background is calculated. The configuration-space metric dependence of the unique effective action in these calculations is investigated. The appearing problems (the configuration-space metric dependence of the physical quantities like induced gravitational constant) are discussed.