The Spectrum of Gravitational Wave Perturbations in the One-Bubble Open Inflationary Universe

We give the initial spectrum of quantized gravitational waves in the context of the one-bubble open inflationary universe scenario. In determining the quantum state after the bubble nucleation we adopt the prescription to require the analyticity of positive frequency functions in half of the Euclidean extension of the background O(3,1)-symmetric spacetime. We find the spectrum is well behaved at the infrared limit and there appears no supercurvature mode. In the thin wall approximation, the explicit form of the spectrum of gravitational wave perturbations is calculated.Comment: 24 pages ptp-tex file, 2 postscript figures. Progress of Theoretical Physics accepted. The ptp-tex style file is available at http://www.yukawa.kyoto-u.ac.j

Super-Horizon Scale Dynamics of Multi-Scalar Inflation

We consider the dynamics of a multi-component scalar field on super-horizon scales in the context of inflationary cosmology. We present a method to solve the perturbation equations on super- horizon scales, i.e., in the long wavelength limit, by using only the knowledge of spatially homogeneous background solutions. In doing so, we clarify the relation between the perturbation equations in the long wavelength limit and the background equations. Then as a natural extension of our formalism, we provide a strategy to study super-horizon scale perturbations beyond the standard linear perturbation theory. Namely we reformulate our method so as to take into account the nonlinear dynamics of the scalar field.Comment: 14 pages, typos corrected, to be published in Prog. Theor. Phys. 99 (1998

Large Angle CMB Anisotropy in an Open Universe in the One-Bubble Inflationary Scenario

We consider an alternative scenario of inflation which can account for a spatially open universe. It is similar to the old inflation in which the bubble nucleation occurs in the sea of false vacuum, but differs from it in that the second slow rollover inflation occurs inside a nucleated bubble. Hence our observable universe is entirely contained in one nucleated bubble. The significance of the scenario is that apart from a variance due to model parameters it gives us a definite prediction on the spectrum of the primordial density perturbations, hence is observationally testable. Here we investigate the spectrum of CMB anisotropies on large angular scales. We find that the contribution from peculiar modes which never appear in the usual harmonic analysis is significant in the case $\Omega_0\lesssim0.1$.Comment: 8 pages, 6 figures, uuencoded compressed PS fil

Gravitational Radiation Reaction to a Particle Motion

In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first one is an extension of the well-known formalism by DeWitt and Brehme developed for deriving the equation of motion of an electrically charged particle. In contrast to the electromagnetic case, in which there are two different charges, i.e., the electric charge and the mass, the gravitational counterpart has only one charge. This fact prevents us from using the same renormalization scheme that was used in the electromagnetic case. To make clear the subtlety in the first approach, we then consider the asymptotic matching of two different schemes, i.e., the internal scheme in which the small particle is represented by a spherically symmetric black hole with tidal perturbations and the external scheme in which the metric is given by small perturbations on the given background geometry. The equation of motion is obtained from the consistency condition of the matching. We find that in both ways the same equation of motion is obtained. The resulting equation of motion is analogous to that derived in the electromagnetic case. We discuss implications of this equation of motion.Comment: 25 pages revtex fil

Vacuum State of the Dirac Field in de Sitter Space and Entanglement Entropy

We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as $m^2/H^2$ becomes small, and the difference is maximal in the massless limit.Comment: 22 pages, 2 figure