Aspectos do nascimento de um universo assintoticamente DeSitter

Abstract

In this dissertation we revised the canonical quantization of General Relativity, up to the derivation of the Wheeler-deWitt equation. Using that theory, we studied a cosmological model described by a closed Friedmann-Robertson-Walker space-time with radiation and a positive cosmological constant. That model describes, at the quantum level, the birth of an asymptotically DeSitter universe through the tunneling process. In our case, the Wheeler-deWitt equation becomes a Schrodinger equation with a potential of the form a x2 — b x4. This potential originates a barrier that the primordial radiation has to tunnel in order to form the material content of our present universe. With the objective of studying the tunneling probability of the universe through this barrier, we solved numerically the Schrodinger equation of our model. Also using numerical methods, we computed the tunneling probability as a function of the mean energy radiation and the cosmological constant, the parameters of our model. We compared our numerical results with the ones calculated using the WKB approximation.