Does a varying speed of light solve the cosmological problems?

We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised Einstein equations for Friedmann universes and show that arbitrary time-variations of c and G never lead to a solution to the flatness, horizon or Λ problems for a theory satisfying the strong energy condition. In order to do so, one needs to construct a theory which does not reduce to the standard one for any choice of time, length and energy units. This can be achieved by breaking a number of invariance principles such as covariance and Lorentz invariance.     

Non-perturbative effects inside the QCD bag

Non-perturbative effects are investigated inside the QCD bag, on which perfectly confining boundary conditions are given. The instanton density is evaluated and used to estimate effective quark-antiquark hamiltonians, as well as the magnitude of chiral symmetry breaking for massless quarks.     

Scale invariance and inflation

A scale invariant model for early universe inflationary cosmology is developed. In order to realize dilatation invariance and spontaneous symmetry breaking we introduce two scalar fields, a dilaton and an inflaton. The scale invariant theory encompasses the Brans-Dicke and induced-gravity models as limiting cases. The model is solved numerically for a wide class of initial conditions. We find that the inflationary epoch is generically characterized by a two phase evolution of the universe: A single or double exponential era and a power-law expansion. Onset of gravity triggers double exponential evolution of the scale factor. We further examine inflation in the Brans-Dicke theory and find that scale invariance is restored in the course of spontaneous symmetry breaking.     

Does proton decay follow the exponential law?

Tetrads cause the breakdown of symmetry in gravitational theories. Their vacuum expected values reduce the symmetry of the vacuum from that of the action to what is global Poincaré invariance at ordinary distances. Gravitational theories can be written in terms of rescaled fields in such a way that the Planck mass never appears. The rescaled fields are dimensionless, except for gauge fields and tetrads, both of which acquire the dimension of mass. The empirical distribution of energy throughout spacetime causes the tetrads to assume vacuum expected values of the order of the Planck mass,m _p . Thus the gravitational constant,G=hc/m _p ² , may be viewed not as a fundamental constant, but as a mass scale that is dynamically determined by the large-scale structure of the universe. Generalized tetrads may also break internal symmetries.     

A dynamical approach to the cosmological constant

This Letter presents an exact analytic solution of a simple cosmological model in presence of both nonrelativistic matter and scalar field where Einstein's cosmological constant Λ appears as an integration constant. Unlike Einstein's cosmological constant ascribed to vacuum energy, the dark energy density and the energy density of the ordinary matter decrease at the same rate during the expansion of the universe. Therefore the model is free of the coincidence problem. Comparing the predictions using this model with the current cosmological observations shows that the results are consistent.     

Calculation of the regularized vacuum energy in cavity field theories

A novel technique based on Schwinger's proper time method is applied to the Casimir problem of the M.I.T. bag model. Calculations of the regularized vacuum energies of massless scalar and Dirac spinor fields confined to a static and spherical cavity are presented in a consistent manner. While our results agree partly with previous calculations based on asymptotic methods, the main advantage of our technique is that the numerical errors are under control. Interpreting the bag constant as a vacuum expectation value, we investigate potential cancellations of boundary divergences between the canonical energy and its bag constant counterpart in the fermionic case. It is found that such cancellations do not occur. Received: 19 March 1999 / Published online: 28 September 1999     

Particle mixing, flavor condensate and dark energy

The mixing of neutrinos and quarks generate a vacuum condensate that, at the present epoch, behaves as a cosmological constant. The value of the dark energy is constrained today by the very small breaking of the Lorentz invariance.     

Scale invariance and spontaneous symmetry breaking

Spontaneous breaking of gauge symmetries is studied in theories with nonlinearly realized scale invariance. The classically sliding vacuum expectation values are fixed through quantum corrections. The anomaly of the dilatation current determines the vacuum energy density as well as the dilaton mass. The coupling of gravity to matter is modified in such a way that the cosmological constant vanishes.     

A model of spontaneous symmetry breakdown in spatially flat cosmological spacetimes

This paper is an elaboration of a previous short exposition of a theory of spontaneous symmetry breaking in a conformally coupled, massless λø⁴ model in a spatially flat Robertson-Walker spacetime. Under the weakened global boundary condition allowing the physical spacetime to be conformal to only a portion of the Minkowski spacetime, the model admits a pair of degenerate vacua in which the ø → ? ø symmetry is spontaneously broken. The model is formulated as a euclidean field theory in a space with a positive-definite metric obtained by analytically continuing the conformal time coordinate. An appropriate time-dependent zero energy solution of the euclidean equation of motion representing the field configuration in the asymmetric vacuum is considered and the corresponding quantum trace anomaly 〈T_μ^μ〉 is computed in the one-loop approximation. The nontrivial infrared behavior of the model due to the singular nature of the classical background field forces a modification of the boundary conditions on the propagator. A general form for an “improved|DD one-loop trace anomaly is found by a simple argument based on renormalization group invariance. Via the Einstein equation, the trace anomaly leads to a self-consistent dynamical equation for the cosmic expansion scale factor. Some physical aspects of the back-reaction problem based on a simple power law model of the expansion scale factor are discussed.     

Conformal Invariance, Accelerating Universe and the Cosmological Constant Problem

We investigate a conformal invariant gravitational model which is taken to hold at early universe. The conformal invariance allows us to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transition, the resulting mass scale introduced by particle physics should have a variable contribution to vacuum energy density. This variation is controlled by the conformal factor which is taken as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.     

Rigid random surfaces at large d

A model of two-dimensional random surfaces with extrinsic curvature energy is studied in the limit where the dimension of bulk space d is large. The large-d effective potential is constructed. For large surface tension the ground state is homogeneous and its properties are studied. For small enough surface tension, non-perturbative instabilities which break translation invariance in the plane of the membrane are shown to occur for large but finite wavelength. The relationships between this model, the bosonic string, the Liouville model and lattive random surface models are discussed.     

General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.     

Chiral bag plus skyrmion hybrid model for nucleons

The chiral bag plus skyrmion hybrid model is studied as a model for nucleons. The hybrid model is solved numerically, where great care has been taken to remove the divergence in the boundary condition at the chiral bag surface for the nonlinear differential equation of the skyrmion. The numerical results for the nucleon energy turn out to be finite for all bag radii, differing from the case of the linearized chiral model. With a suitable choice of the bag parameter (volume term), the nucleon mass, radius and the axial vector coupling constant g_A come out to be very promising.     

Breathing motion of a kink-bag system in (1 + 1) dimensions: Inertia of the vacuum confined in a bag

We examine the breathing motion of a (1 + 1)-dimensional hybrid bag where the confined quarks are coupled with a solitonic chiral field at the bag boundary. The hybrid bag is a toy model for the (1 + 3)-dimensional skyrmion-bag system and its breathing motion has close connection with the excited states of a nucleon such as the Roper resonance. The collective lagrangian for the motion is derived microscopically by focusing on the polarized Dirac sea inside the bag. The mass parameter of the motion is decreased compared with the MIT-bag one owing to the negative contribution from the inertia of the confined vacuum. As a result, the spectra of the motion do not have too low excitation energies despite that the potential energy surface is softened by the vacuum effect.     

Vacuum energy in the presence of dielectric and conducting surfaces

The polarization of the electromagnetic vacuum is examined in the neighborhood of dielectric and conducting surfaces and the energy associated with this polarization is shown to depend on a cutoff related to the microstructure of the boundary. The appearance of the cutoff permits the vacuum energy to be expressed in terms of a surface tension and certain higher shape tensions. For the case of a dielectric boundary the surface tension reproduces the Schmitt-Lucas formula which accounts reasonably for the observed surface tensions of many materials. The curvature tension is also calculated and it seems the effect of this energy may well be accessible to experimental verification. For the case of perfectly conducting surfaces the first four shape tensions are calculated. It is shown that previous calculations of the vacuum energy due to perfectly conducting surfaces are in error and these errors are corrected.     

A model of the universe with decaying vacuum energy

The consequences of taking the total active gravitational mass of the universe phasewise constant together with a decaying vacuum energy in the background of Robertson-Walker space-time are investigated. The model so determined admits a contracted Ricci-collineation along the fluid flow vectorν ⁱ. It is geometrically closed but ever-expanding and does not possess the initial singularity, horizon, entropy, monopole or cosmological constant problems of the standard big bang cosmology. Estimates of the present matter; radiation and vacuum energy densities, the age of the universe and the present values of the deceleration parameter and the scale factor are also obtained.     

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.     

Quintessential adjustment of the cosmological constant

We construct a time dependent adjustment mechanism for the cosmological "constant" which could be at work in a late Friedmann-Robertson-Walker universe dominated by quintessence and matter. It makes use of a Brans-Dicke field that couples to the evolving standard-model vacuum energy density. Our explicit model possesses a stable late-time solution with a fixed ratio of matter and field energy densities. No fine-tuning of model parameters or initial conditions is required.     

Semiclassical solutions ofOSp(N,4) supersymmetry 0

This work analyzes the connection between the so-called reflective boundary conditions and the spontaneous breaking of supersymmetry in anti-de Sitter background space. The one-loop effective potential of the Wess-Zumino model is computed using the supersymmetry invariant Pauli-Villars regularization procedure. The effect of the background geometry is determined exactly. It is shown that supersymmetry is preserved to the one-loop order at each classically supersymmetric extremum of the effective potential. Depending on the reflective boundary conditions chosen, quantum shifts in theA-field andB-field vacuum solutions are exhibited.