CITA Research September 2002 - August 2003
Early Universe and General Relativity

In recent years, CITA has been a center of activity for studies of the early universe. Kofman and collaborators Frolov and Felder have been studying the implications of string theory and the braneworld scenario for the expansion of the universe in its early stages, and the generation of scalar and tensor perturbations. Beloborodov and Frolov has also conducted research in classical general relativity.

Thermodynamical aspects of quasi-de Sitter geometry

Lev Kofman and Andrei Frolov considered thermodynamical aspects of the quasi-de Sitter geometry of the inflationary universe. They calculated the energy flux of the slowly rolling background scalar field through the quasi-de Sitter apparent horizon and set it equal to the change of the entropy (1/4 of the area) multiplied by the temperature, dE=TdS. Remarkably, this thermodynamic law reproduces the Friedmann equation for the rolling scalar field. Next they added inflaton fluctuations which generate scalar metric perturbations. Metric perturbations result in a variation of the area entropy. Again, the equation dE=TdS with fluctuations reproduces the linearized Einstein equations. In this picture, as long as the Einstein equations hold, holography does not put limits on the quantum field theory during inflation. Due to the accumulating metric perturbations, the horizon area during inflation randomly wiggles with dispersion increasing with time. They discussed this in connection with the stochastic description of inflation.

Dynamics of the rolling tachyon

Kofman studied the dynamics of the rolling tachyon which forms after the antibrane annihilation. This is a vital part in the string theory of cosmology inflation.

Properties of Schwarzschild black holes

Andrei Frolov and Valeri Frolov (University of Alberta) investigated properties of a 4-dimensional Schwarzschild black hole in a spacetime where one of the spatial dimensions is compactified. As a result of the compactification the event horizon of the black hole is distorted. They used Weyl coordinates to obtain the solution describing such a distorted black hole. This solution is a special case of the Israel-Khan metric. They studied the properties of the compactified Schwarzschild black hole, and developed an approximation which allows one to find the size, shape, surface gravity and other characteristics of the distorted horizon with a very high accuracy in a simple analytical form. They also discussed possible instabilities of a black hole in the compactified space.

Numerical Studies of Braneworld Dynamics

Working with Johannes Martin, Andrei Frolov, Lev Kofman, and Marco Peloso of CITA, Felder developed a program for calculating the time evolution of a braneworld system. The program self-consistently solves the Einstein equations in the bulk and junction conditions on the branes. Using this code they were able to show that such systems will generically tend to have multiple metastable states corresponding to different effective cosmological constants on the brane. A transition from such a metastable state to the ground state could account for the occurrence and end of inflation. This program is being made publicly available under the name BRANECODE.

Origin of the acceleration of the universe

Together with E. Poppitz (Toronto U.) Peloso discussed the possibility that the present acceleration of the universe is driven by the evolution of shape moduli in sub-millimeter extra dimensional scenarios. The potential for the moduli is protected from destabilizing corrections (the main problem in models of quintessence) by locality and diffeomorphism invariance of the higher dimensional theory.

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