Entropy generation in the early universe by dissipative processes near the Higgs phase transition

We suggest that the anomalous dissipation near the Higgs phase transition in the early Universe might be one of the non-negligible mechanisms to produce the cosmic entropy. Such processes may well generate a value of S comparable with the presently observed result. In a simplified σ-model the qualitative relations between the specific entropy and the mass and self-interaction of the vacuum field have been obtained.     

Quantum theory of dissipative processes: The Markov approximation revisited

Adopting the standard mathematical framework for describing reduced dynamics, we derive two formal identities for the density operator of an open quantum system. Each of these is equivalent to the old Nakajima-Zwanzig equation. The first identity is local in time. It contains the inverse of the dynamical map which govern the evolution of the density operator. We indicate a time interval on which this inverse exists. The second identity constitutes a suitable starting point for going beyond the Markov approximation in a controlled way. On the basis of the Bloch equations we argue once more that in studying quantum dissipation one has to pay attention to the von Neumann conditions. In the Nakajima-Zwanzig equation we make the first Born approximation. The ensuing master equation possesses the correct weak-coupling limit. While proving this rather obvious but at the same time important statement, we elucidate the mathematical methods which underlie the weak-coupling limit. Moving to a two-dimensional Hilbert space, we find that both for short and for long times our approximate master equation respects the von Neumann conditions. Assuming exponential decay for correlation functions, we propose a physical limit in which the solutions for the density operator become Markovian in character. We confirm the well-known statement that, as seen from a macroscopic standpoint, the system starts from an effective initial condition. The approach to equilibrium is exponential. The accessory relaxation constants can differ from the usual Bloch parameters and by more than 50%.     

Models of the universe containing matter and gravitational radiation

The manner in which a field of gravitational radiation modifies the cosmological background space-time of the model universe containing it is considered. The cosmological equations for the models are solved and a number of examples of the resulting universes are presented in diagrammatic and tabular form.     

Cylindrical gravitational wave in Melvin universe

In the paper, a solution of the problem of the propagation of a cylindrical gravitational wave in the general theory of relativity in Melvin's magnetic universe is obtained by application of the Harrison method to the Einstein-Rosen wave solution. The solution found here illustrates the nonlinear process of transforming a cylindrical gravitational wave in a transverse static electromagnetic field into an electromagnetic wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 24–28, December, 1979.The author expresses his gratitude to the participants of the seminar of Professor D. D. Ivanenko for discussing the results of the paper.     

Quantum cosmology of the brane universe

We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-de Sitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the (3+1)-dimensional case. The Wheeler-DeWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.     

Hydrogen-like atom in the gravitational field of the universe

Exact solutions are obtained for a hydrogen-like atom in an external cosmological field of the closed and open universe. It is found that in the closed model, in addition to a gravitational analog of the Stark effect, there is a new effect-atom ionization by the gravitational field. In the open model, discrete and continuous spectra are obtained; furthermore, discrete spectrum consists of a finite number of states, and in the continuous spectrum the effect of the proton field is preserved despite absence of a bound state. It is shown that transition frequency depends on the radius (age) of the universe in both models, and, consequently, a hydrogen-like atom, in principle, cannot serve as a reference of time-frequency-length.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 55–59, January, 1985.     

New gravitational tests of early universe cosmology

Gravitational waves and lenses were among the earliest predictions of general relativity. I demonstrate here how both these phenomena can, in conjunction with newly discovered astrophysical objects, be used to test fundamental aspects of early universe cosmology, including (a) scenarios for galaxy formation, and (b) nonadiabatic expansion before and after nucleosynthesis.Research supported in part by the N.S.F. under Grant No. PHY-82-15249.     

Quantum mechanics of the early universe

Quantum tunneling of the universe from nothing into a de Sitter vacuum, interpreted as the birth of the universe from a vacuum, is considered. Vilenkin's results are generalized by allowing for strings, domain walls, and various kinds of compressed matter that contribute to the potential through which the tunneling occurs. The energy spectrum of the universe in the quantum pre-de Sitter stage, the coefficient of passage through the potential barrier, which describes the probability of birth of the universe, and the conditions of applicability of the quasi-classical approximation in the calculation of these quantities are found.Brainstorm MNTP, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 78–82, April, 1995.     

Particle decay and bulk dissipative stress in the early universe

In this paper we show that the combined action of particle decay and a physically motivated dissipative bulk stress can lead to a period of generalized inflation and temperature increase. This effect may have occurred at the baryogenesis era.     

Quantum gravitational optics

In quantum theory, the curved spacetime of Einstein's general theory of relativity acts as a dispersive optical medium for the propagation of light. Gravitational rainbows and birefringence replace the classical picture of light rays mapping out the null geodesics of curved spacetime. Even more remarkably, superluminal propagation becomes a real possibility, raising the question of whether it is possible to send signals into the past. In this article, we review recent developments in the quantum theory of light propagation in general relativity and discuss whether superluminal light is compatible with causality.     

Quantum gravitational bubbles

Spacetime is expected to have a “foamlike” structure on scales of the Planck length or less with high curvatures and complicated topology. This foam can be thought of as being built out of three basic kinds of units or “gravitational bubbles”, CP², S² × S² and K3. We investigate the propagation of particles in simple models of the first two types of bubble. The non-trivial topologies of the bubbles introduce extra singularities into the Green functions. These make large contributions to the S-matrix for scalar particles but only small contributions for $\text{spin}\text{-}\text{1}\text{2}$ or 1 particles at energies small compared to the Planck length. These results suggest that there is no inconsistency between the spacetime foam picture and everyday observations from which spacetime appears nearly flat, because all the elementary particles we have observed have spin $\text{1}\text{2}$ or greater. They do, however, suggest that Higgs scalar fields, if they exist at all, are probably bound states of higher spin particles rather than being elementary fields. Further developments may enable one to calculate processes in which quantum coherence is lost and intrinsic entropy is produced.     

Growth of a dissipative universe and the limits of Newtonian cosmology

In closed model universes assumed to bounce at some minimum radius, dissipation causes the amplitude of the oscillations to grow. This well-known fact of relativistic cosmology is counterintuitive. Since Newtonian models correspond closely to relativistic ones when there is no dissipation, we examine dissipative Newtonian models, and note the peculiarly relativistic ideas which must be introduced to obtain correct results.     

Tachyon warm-inflationary universe model in the weakly dissipative regime

The warm-inflationary universe model in a tachyon field theory is studied in the weakly dissipative regime. We develop our model for an exponential potential and the dissipation parameter Γ=Γ ₀=constant. We describe scalar and tensor perturbations for this scenario.     

Quantum dissipative Higgs model

By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.     

Time dependent gravitational potential in the universe and some consequences

In this paper, assuming a linear change of the gravitational potential V in the universe, i.e. , some consequences are obtained. 1. The Hubble red shift is explained by the potential difference between the considered galaxy long time ago and the observer at this epoch. 2. The anomalous acceleration a _P from the spacecraft Pioneer 10 and 11 [1] is explained. 3. The deformations of the trajectories of planets are studied. It is shown that the planetary orbits are not axially symmetric and the angle from the perihelion to the aphelion is , while the angle from the aphelion to the perihelion is , where is the orbital period. There is no perihelion precession caused by the time dependent gravitational potential V. The quotient of two consecutive orbital periods ₁ and ₂ is equal to This formula is tested for the pulsars B1885+09 and B1534+12, and the results are good.This revised version was published online in April 2005. The publishing date was inserted.     

Viscous phenomena and entropy production in the early universe

We calculate shear and bulk viscosity of the cosmological fluid for the early universe. Integrating the gravitational equations for isotropic models, we find that photon entropy increases by 0.11% due to the bulk viscosity in the lepton and plasma eras.     

Quantum space-time and gravitational consequences

Relativistic particle dynamics and basic physical quantities for the general theory of gravity are reconstructed from a quantum space-time point of view. An additional force caused by quantum space-time appears in the equation of particle motion, giving rise to a reformulation of the equivalence principle up to values ofO(L ²), whereL is the fundamental length. It turns out that quantum space-time leads to quantization of gravity, i.e., the metric tensorg _v () becomes operator-valued and is not commutative at different pointsx andy in usual space-time on a large scale, and its commutator depending on the vielbein field (gaugelike graviton field) is proportional toL ² multiplied by a translation-invariant wave function propagated between pointsx andy . In the given scheme, there appears to be an antigravitational effect in the motion of a particle in the gravitational force. This effect depends on the value of particle mass; when a particle is heavy its free-fall time is long compared to that for a light-weight particle. The problem of the change of time scale and the anisotropy of inertia are discussed. From experimental data from testing of the latter effect it follows thatL10^–22cm.     

Quantum driven bounce of the future universe

It is demonstrated that due to back-reaction of quantum effects, expansion of the universe stops at its maximum and takes a turn around. Later on, it contracts to a very small size in finite future time. This phenomenon is followed by a “bounce” with re-birth of an exponentially expanding non-singular universe.