The dynamics of the early universe in a model with radiation and a generalized Chaplygin gas: Early universe with radiation and a generalized Chaplygin gas

The early universe is modeled through the quantization of a Friedmann-Robertson-Walker model with positive curvature of the spatial hypersurfaces. In this model, the universe is filled by two fluids: radiation and a generalized Chaplygin gas. The quantization of this model is made following the prescriptions due to J. A. Wheeler and B. DeWitt. Using the Schutz's formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time-dependent Schrodinger equation, which rules the dynamics of the early universe, under the action of an effective potential Veff. That potential depends on three parameters. Depending on the values of these parameters, Veff may have two different shapes. Veff(a) may have the shape of a barrier or the shape of a well followed by a barrier. We solve, numerically, the appropriate time-dependent Schrodinger equation and obtain the time evolution of an initial wave function, for both cases. These wave functions satisfy suitable boundary conditions. For both shapes of Veff, we compute the tunneling probability, which is a function of the mean kinetic energy associated to the radiation energy Em and of the three parameters of the generalized Chaplygin gas: alpha, A and B. The tunneling probabilities, for both shapes of Veff, indicate that the universe should nucleate with the highest possible values of Em, alpha, A and B. Finally, we study the classical universe evolution after the wavefunction has tunneled Veff. The calculations show that the universe may emerge from the Planck era in an inflationary phase.

Automated summary

The study focuses on quantizing the dynamics of the early universe and numerically solving for the time evolution of the wave function and tunneling probability. The results suggest that the universe should nucleate with the highest values of energy and parameters, and may enter an inflationary phase afterwards.