Inflation and numerical relativity

A fully general relativistic computer code, which can simulate a plane-symmetric space time filled with a perfect fluid and a scalar field, was developed. The code is based on an earlier code by Centrella and Wilson, which was without the scalar field. Inhomogeneity is allowed in one space direction. The code is used to simulate phase transitions in the very early universe. Such phase transitions are due to a scalar field, the Higgs field. Because of the nonzero vacuum energy density of the old phase, the scalar field can have interesting effects on the spacetime curvature. The general relativistic equations are cast into a 3 + 1 form suitable for numerical solution, according to the ADM method. The computer code is described and results of the code tests are given. Simulations are presented on the entry to the inflationary stage of the universe, starting with inhomogeneous initial data for the Higgs field. Inflation is realized in a model with a Coleman-Weinberg type potential with σ = 0.1 m/sub pi/ and λ ≤ 10-2, or with σ = 0.01 m/sub pi/ and λ ≤ 10-5. For larger values of λ, the initial inhomogeneity leads to early domain formation, which prevents inflation. General relativistic vacuum bubbles and special relativistic detonation and deflagration bubbles are studied analytically. Numerical simulation on phase transition bubbles and their effects on space time geometry are presented within a plane symmetric framework. Limitations of the present code and the reasons behind them are discussed