Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.     

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.     

Gravitation and spontaneous symmetry breaking

It is pointed out that the Higgs field may be supplanted by an ordinary Klein-Gordon field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theories. In the theory presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature.Research supported by the Arnow Chair in Astrophysics.     

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.     

Decay of cosmological constant in self-consistent inflation

The symmetric vacuum state in gauge theories with spontaneous symmetry breaking is symmetric in both internal and space-time variables. We consider this vacuum state as a Bose condensate of physical Higgs particles, defined over an asymmetric vacuum state, and identify the energy density of their self-interaction with the cosmological constant in the Einstein equation. In this picture, spontaneous symmetry breaking proceeds as decay. Decoherence of coherent oscillations of a scalar field in the course of decay provides the effective mechanism for damping of coherent oscillations, leading to the regime of slow evaporation of a Bose condensate. This mechanism is responsible for self-consistent inflation without fine-tuning of the potential parameters. The physical self-consistency in this model is provided by incorporating the origin of the cosmological constant in the dynamics of spontaneous breaking of particle symmetries. Received: 28 September 2000 / Revised version: 16 January 2001 / Published online: 25 April 2001     

Increasing vacuum solutions in induced gravitation

It is shown that a solution of the form R(ν)=0 (R is the space-time curvature) exists for a vacuum solution (the field fluctuations are assumed zero, and only the ground state with the minimum effective potential energy remains) in the initial stage with consideration of the effect of spontaneous symmetry breaking for a scalar field with the “wrong sign” of the mass term and the conformal factor. For a spherically symmetric metric in vacuum, a solution increasing as a square of the distance and proportional to the square of the Higgs boson mass exists. A. A. Fridman Theoretical Physics Laboratory. Translated from Izvestiya Vysshikh Uchebhykh Zavedenii, Fizika, No. 4, pp. 34–38, April, 2000.     

Signature change, vacuum condensation and cosmological constant

We proposes an alternative model of duality symmetry, based on the previously obtained divergence theory, including an scalar field, an internal vector and a metric signature. At some small scale an effective scalar field equation has appeared whose potential acts like a Higgs one, where the metric signature plays the role of an order parameter. Non-vanishing Vacuum condensation of this Higgs field occurs once a signature change from Euclidean to Lorentzian is formed. The mass scale of Higgs field excitations around this vacuum may contribute, in the Lorentzian sector, to the cosmological constant, in agreement with observations.     

THE PROBLEM OF THE COSMOLOGICAL CONSTANT

The cosmological term is necessaritly vanishing in a conformal gravitational theory, and the sum of the induced cosmological constants of all the brocken gauge symmetries cancels the curvature of the background spacetime. Thus the sum of all the cosmological constants is vanishing when the background spacetime is Minkowskian. Furthermore, the spontaneous breaking of a gauge symmetry through the Higgs mechanism is always accompanied by a phase transition of the background spacetime.     

Renormalization of Quantum Field Theory in Curved Space-Time and Renormalization Group Equations

The structure of quantum field theory renormalization in curved space-time is investigated. The equations allowing us to investigate the behaviour of vacuum energy and vertex functions in the limit of small distances in the external gravitational field are established. The behaviour of effective charges corresponding to the parameters of nonminimal coupling of the matter with the gravitational field is studied and the conditions under which asymptotically free theories become asymptotically conformally invariant are found. The examples of asymptotically conformally invariant theories are given. On the basis of a direct solution of renormalization group equations the effective potential in the external gravitational field and the effective action in the gravity with the high derivatives are obtained. The expression for the cosmological constant in terms of R²-gravity Lagrangian parameters is given which does not contradict the observable data. Renormalization and renormalization group equations for the theory in curved space-time with torsion are investigated.     

A Classical Cosmological Model for Triviality

The aim of this paper is to study the triviality of λ ϕ⁴ theory in a classical gravitational model. Starting from a conformal invariant scalar tensor theory with a self-interaction term λ ϕ⁴, we investigate the effect of a conformal symmetry breaking emerging from the gravitational coupling of the large-scale distribution of matter in the universe. Taking in this cosmological symmetry breaking phase the infinite limit of the maximal length (the size of the universe) and the zero limit of the minimal length (the Planck length) implies triviality, i.e. a vanishing coupling constant λ. It suggests that the activity of the self-interaction term λ ϕ⁴ in the cosmological context implies that the universe is finite and a minimal fundamental length exists.     

Quantum gravity,the origin of time and time's arrow

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature T_c below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T<T_c, allowing a semiclassical WKB approximation to the wave function. The conservation of energy is spontaneously violated for T>T_c, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures.     

Conformal Anomaly and Large-ScaleGravitational Coupling

We present a model in which the breakdown of conformal symmetry of a quantumstress-tensor due to the trace anomaly is related to a cosmological effect in agravitational model. This is done by characterizing the traceless part of thequantum stress-tensor in terms of the stress-tensor of a conformal invariantclassical scalar field. We introduce a conformal frame in which the anomaloustrace is identified with a cosmological constant. In this conformal frame weestablish the Einstein field equations by connecting the quantum stress-tensorwith the large-scale distribution of matter in the universe.     

Higgs-field gravity within the standard model

Within the framework of the Glashow-Salam-Weinberg model it is shown that the Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles which become massive by the ground state of the Higgs field after symmetry breaking.     

A unified conformal model for fundamental interactions without dynamical Higgs field

A Higgsless model for strong, electroweak and gravitational interactions is proposed. This model is based on the local symmetry group SU(3)×SU(2)_L×U(1)×C,where C is the local conformal symmetry group. The natural minimal conformally invariant form of total Lagrangian is postulated. It contains all standard model fields and gravitational interaction. Using the unitary gauge and the conformal scale fixing conditions, we can eliminate all four real components of the Higgs doublet in this model. However, the masses of vector mesons, leptons, and quarks are automatically generated and are given by the same formulas as in the conventional standard model. In this manner one gets the mass generation without the mechanism of spontaneous symmetry breaking and without the remaining real dynamical Higgs field. The gravitational sector is analyzed, and it is shown that the model admits in the classical limit the Einsteinian form of gravitational interactions.     

Dynamical Conformal Transformation and Classical Euclidean Wormholes

We investigate the necessary condition for the existence of classical Euclidean wormholes in a conformally non-invariant gravitational model minimally coupled to an scalar field. It is shown that while the original Ricci tensor with positive eigenvalues does not allow the Euclidean wormholes to occur, under dynamical conformal transformations the Ricci tensor, with respect to the original metric, is dynamically coupled with the conformal field and its eigenvalues may become negative allowing the Euclidean wormholes to occur. Therefore, it is conjectured that dynamical conformal transformations may provide us with effective forms of matter sources leading to Euclidean wormholes in conformally non-invariant systems.     

A conformai,symmetry broken model for gravity

Starting from Padmanabhan's fully conformally invariant action, we obtain gravity as a spontaneously broken theory. Newton's constant and the cosmological constant follow from the breakdown of the conformal symmetry at the tree approximation. For small oscillation of the scalar field about the fundamental state, the matter field degenerates into two decoupled fields.     

Inflationary universe without GUTs

The existence of a primordial inflationary era is unavoidable due to the puzzling nature of semiclassical gravitation, regulated by Einstein's equations and the laws of quantum mechanics. This interaction appears to be controlled by a mass-dependent effective gravitational coupling constant. The latter undergoes an unexpected transition from a classical gravitational attractive to an antigravitational repulsive regime when the corresponding mass of a quantum matter field passes through a definite threshold. This induces in turn a gravitational, spontaneously broken symmetry phenomenon responsible for the presence of an unusual non-Minkowskian ground state: the inflationary de Sitter space-time. This then acquires the status of the primordial cosmological vacuum, the generic configuration of our cosmological history.     

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.     

Conformally coupled scalar field solutions and the cosmological constant

Solutions are presented for a scalar field coupled conformally to Einstein gravity with a nonvanishing cosmological constant, in the case that the spacetime metric is spatially homogeneous and isotropic. Since the cosmological constant destroys the conformal invariance of the action, these solutions cannot be obtained by solving the flat space wave equation for the scalar field. It turns out that the metric is determined entirely by the cosmological constant, while the scalar field acquires an apparent mass squared which is proportional to the cosmological constant. It is conjectured that the cosmological constant in the universe at present may thus be disguised as the mass of some scalar field.     

Spontaneous symmetry breaking due to polarization corrections

A model of self-interacting scalar and gravitational fields is constructed, in which the vacuum state with spontaneously broken symmetry arises as a solution of the field equations. The gravitational Lagrangian containing curvature-squared contributions is treated in the first-order formalism. The problems of cosmological singularities and conformal anomalies are discussed. In the case of vanishing Weyl tensor and constant scalar curvature, the curvature-squared contributions may be interpreted as being generated by the vacuum polarization, also in first-order formalism.