Paper detail

The dynamics of the early universe and the initial conditions for inflation in a model with radiation and a Chaplygin gas

The modeling of the early universe is done through the quantization of a Friedmann-Robertson-Walker model with positive curvature. The material content consists of two fluids: radiation and Chaplygin gas. The quantization of these models is made by following the Wheeler and DeWitt's prescriptions. Using the Schutz formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schrödinger equation, which rules the dynamics of the early universe, under the action of an effective potential $V_{ef}$. Using a finite differences method and the Crank-Nicholson scheme, in a code implemented in the program OCTAVE, we solve the corresponding time dependent Schrödinger equation and obtain the time evolution of a initial wave packet. This wave packet satisfies appropriate boundary conditions. The calculation of the tunneling probabilities shows that the universe may emerge from the Planck era to an inflationary phase. It also shows that, the tunneling probability is a function of the mean energy of the initial wave packet and of two parameters related to the Chaplygin gas. We also show a comparison between these results and those obtained by the WKB approximation.