Choptuik scaling in null coordinates

A numerical simulation is performed of the gravitational collapse of a spherically symmetric scalar field. The algorithm uses the null initial value formulation of the Einstein-scalar equations, but does {\it not} use adaptive mesh refinement. A study is made of the critical phenomena found by Choptuik in this system. In particular it is verified that the critical solution exhibits periodic self-similarity. This work thus provides a simple algorithm that gives verification of the Choptuik results.Comment: latex (revtex), 6 figures included in the fil

Onset of inflation in inhomogeneous cosmology

We study how the initial inhomogeneities of the universe affect the onset of inflation in the closed universe. We consider the model of a chaotic inflation which is driven by a massive scalar field. In order to construct an inhomogeneous universe model, we use the long wavelength approximation ( the gradient expansion method ). We show the condition of the inhomogeneities for the universe to enter the inflationary phase.Comment: 22 pages including 12 eps figures, RevTe

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

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

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

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

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.

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