Semiclassical corrections to the Einstein equation and Induced Matter Theory

The induced Einstein equation on a perturbed brane in the Induced Matter Theory is re-analyzed. We indicate that in a conformally flat background, the local quantum corrections to the Einstein equation can be obtained via the IMT. Using the FRW metric as the 4D gravitational model, we show that the classical fluctuations of the brane may be related to the quantum corrections to the classical Einstein equation. In other words, the induced Einstein equation on the perturbed brane can correspond with the semiclassical Einstein equation.     

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

Bouncing cosmologies

We review the general features of nonsingular universes (i.e. those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of perturbations.     

Kaluza-Klein cosmologies

In generalized Kaluza-Klein theories the scale set by the size of the extra space-dimensions is close to the grand unification scale of supersymmetric GUT's with minimal number of Higgs supermultiplets. In view of this observation, we explore cosmologies in which the “effective” dimensionality of space depends on time. Such cosmologies are studied in higher-dimensional Jordan-Brans-Dicke theories, and in 10- and 11-dimensional supergravity. The preferential expansion of three space-like dimensions is noted in the latter theory. Cosmology in pure higher-dimensional Einstein theory, where there is no preferential expansion of three space-like dimensions, has been discussed by Chodos and Detweiler.     

Quantum string cosmologies

Different models of quantum string minisuperspaces for both isotropic and anisotropic geometries are presented. As for the isotropic case the general model of axion‐dilaton cosmology of arbitrary curvature is studied and solved explicitly. In the anisotropic case Bianchi type I and IX and Kantowski‐Sachs geometries are investigated. A short review of string cosmology is given with the emphasis on its “graceful‐exit” problem. The problems of boundary conditions, wave packets in minisuperspace and possible implications for the arrow of time in cosmology are briefly discussed.     

Semiclassical approach to time-dependent tunnelling

We present an exact time-dependent semiclassical formulation of the dynamics of a -atom subjected to an oscillating electric field. Through a simple approximation the results of Ergenzinger's more intuitive analysis are obtained. We also comment on the important role played by the imaginary tunnelling time , which is quite distinct from the usual adiabatic tunnelling time. Received: 24 April 2001 / Revised version: 15 May 2001 / Published online: 3 August 2001     

Electromagnetic Bianchi cosmologies

All exact solutions of the Einstein-Maxwell equations of Bianchi type-I which are of physical importance have been found. The solutions represent non-locally rotationally symmetric universes with source-free electromagnetic fields and the matter content is a perfect fluid, with equation of state p=(γ?1)?(1?γ?2). Non-titled Bianchi type-II models are integrated for perfect fluid matter for all values of γ.     

More supergravity cosmologies

We present new non-trivial cosmological d=11 supergravity Friedmann-Robertson-Walker-Bianchi solutions with a time-dependent cosmological term.     

Anisotropic supergravity cosmologies

Anisotropic cosmologies of Bianchi types I, II, VI₀, VII₀, VIII and IX are studied in the bosonic sector of d = 11 supergravity. Exact solutions are given for all types in s = 4 dimensions coupled to the “round” (d ? s = 7) seven-sphere solutions due to Freund, Rubin, Duff and Pope, and Englert. The generalized Kasner, the Taub-NUT-de Sitter and some “mixmaster” solutions with a cosmological constant are derived. In addition, we wish to point out that the isotropic solution given recently by Myung and Kim does not exist. Another inconsistent solution was also given by Gleiser et al.     

Inhomogeneous two-fluid cosmologies

A new class of expanding cosmological solutions is derived. The matter content of these models is a mixture of two interacting simple fluids: the first one, homogeneous and isotropic with equation of statep = (-1), the dynamics of which is given by the FRW equation and the second one an inhomogenous dust. The limiting case of two dusts corresponds to the Szekeres' universes of class II. A large subclass of the models evolve to a FRW phase for all physically meaningful values of the polytropic index and the curvature parameterk. A gauge condition, under which the metric is invariant, is shown to exist for k0. In particular, it explains why the parabolic model is a peculiar solution in the class found by Szekeres.On leave from Departamento de Fisica Teórica e Experimental Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil.