Inhomogeneity of Spatial Curvature for Inflation

We study how the initial inhomogeneities of the spatial curvature affect the onset of inflation in the closed universe. We consider a cosmological model which contains a radiation and a cosmological constant. In order to treat the inhomogeneities in the closed universe, we improve the long wavelength approximation such that the non-small spatial curvature is tractable in the lowest order. Using the improved scheme, we show how large inhomogeneities of the spatial curvature prevent the occurrence of inflation.Comment: 17 pages, revtex, 6 figures included using eps

Global phase time and path integral for string cosmological models

A global phase time is identified for homogeneous and isotropic cosmological models yielding from the low energy effective action of closed bosonic string theory. When the Hamiltonian constraint allows for the existence of an intrinsic time, the quantum transition amplitude is obtained by means of the usual path integral procedure for gauge systems.Comment: 12 pages, added reference

Choptuik scaling in six dimensions

We perform numerical simulations of the critical gravitational collapse of a spherically symmetric scalar field in 6 dimensions. The critical solution has discrete self-similarity. We find the critical exponent \gamma and the self-similarity period \Delta.Comment: 8 pages, 3 figures RevTe

A Comment on Junction and Energy Conditions in Thin Shells

This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs of mass energy densities in thin shells at the junction depend not only on the orientations of the normals and it is useful therefore to discuss the sign separately. Calculations gain in clarity by not choosing the orientations in advance. Simple examples illustrate our point and complete previous classifications of spherical thin shells in spherically symmetric spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte

Inflationary Initial Conditions Consistent with Causality

The initial condition problem of inflation is examined from the perspective of both spacetime embedding and scalar field dynamics. The spacetime embedding problem is solved for arbitrary initial spatial curvature Omega, which generalizes previous works that primarily treat the flat case Omega=1. Scalar field dynamics that is consistent with the embedding constraints are examined, with the additional treatment of damping effects. The effects of inhomogeneities on the embedding problem also are considered. A category of initial conditions are identified that are not acausal and can develop into an inflationary regime.Comment: 9 pages, 3 figures. Minor changes, matches version to appear in Physical Review

Numerical Study of Inhomogeneous Pre-Big-Bang Inflationary Cosmology

We study numerically the inhomogeneous pre-big-bang inflation in a spherically symmetric space-time. We find that a large initial inhomogeneity suppresses the onset of the pre-big-bang inflation. We also find that even if the pre-big-bang inflationary stage is realized, the initial inhomogeneities are not homogenized. Namely, during the pre-big-bang inflation ``hairs''(irregularities) do not fall, in sharp contrast to the usual (potential energy dominated) inflation where initial inhomogeneity and anisotropy are damped and thus the resulting universe is less sensitive to initial conditions.Comment: 12 pages + 14 figures, to be published in Phys.Rev.

Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation

We study the Einstein-Klein-Gordon equations for a convex positive potential in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing the inherent properties of the system of differential equations, the study of the asymptotic behaviors of the solutions and their stability is done for an exponential potential. The results are compared with those of Burd and Barrow. In contrast with their results, we show that for the BI case isotropy can be reached without inflation and we find new critical points which lead to new exact solutions. On the other hand we recover the result of Burd and Barrow that if inflation occurs then isotropy is always reached. The numerical integration is also done and all the asymptotical behaviors are confirmed.Comment: 22 pages, 12 figures, Self-consistent Latex2e File. To be published in Phys. Rev.

Semiclassical Effects and the Onset of Inflation

We present a class of exact solutions to the constraint equations of General Relativity coupled to a Klein - Gordon field, these solutions being isotropic but not homogeneous. We analyze the subsequent evolution of the consistent Cauchy data represented by those solutions, showing that only certain special initial conditions eventually lead to successfull Inflationary cosmologies. We argue, however, that these initial conditions are precisely the likely outcomes of quantum events occurred before the inflationary era.Comment: 22 pages, file written in RevTe

Centrifugal force induced by relativistically rotating spheroids and cylinders

Starting from the gravitational potential of a Newtonian spheroidal shell we discuss electrically charged rotating prolate spheroidal shells in the Maxwell theory. In particular we consider two confocal charged shells which rotate oppositely in such a way that there is no magnetic field outside the outer shell. In the Einstein theory we solve the Ernst equations in the region where the long prolate spheroids are almost cylindrical; in equatorial regions the exact Lewis "rotating cylindrical" solution is so derived by a limiting procedure from a spatially bound system. In the second part we analyze two cylindrical shells rotating in opposite directions in such a way that the static Levi-Civita metric is produced outside and no angular momentum flux escapes to infinity. The rotation of the local inertial frames in flat space inside the inner cylinder is thus exhibited without any approximation or interpretational difficulties within this model. A test particle within the inner cylinder kept at rest with respect to axes that do not rotate as seen from infinity experiences a centrifugal force. Although the spacetime there is Minkowskian out to the inner cylinder nevertheless that space has been induced to rotate, so relative to the local inertial frame the particle is traversing a circular orbit.Comment: 12 pages, 2 figure