Quantizacão do modelo de mini-superespaço de Friedmann-Robertson-Walker permeado por poeira e uma constante cosmológica

Abstract

In this work we apply the canonical formulation of quantum cosmology to quantize the spatially at Friedmann-Robertson-Walker cosmological model with dust and a cosmological constant. The classical solutions with [Lambda] < 0 and [Lambda] > 0 describe, respectively, a universe eternally oscillating between a singular beginning and a singular end (Big Bang and Big Crunch) and a universe that expands forever from a singular beginning. In the vicinity of these singularities, the energy scale becomes comparable to the Planck scale and the intensity of the gravitational field becomes comparable to the other fundamental interactions, suggesting that quantum effects become increasingly important. Moreover, quantum effects can lead to changes in the dynamics of the universe during the later stages of its evolution or even throughout its evolution since in some cases quantum cosmological models present quantum behavior for large scale factor. After writing the Hamiltonian formulation for general relativity and a relativistic perfect fluid, the latter described by velocity potentials, which allows us to associate a time variable to a degree of freedom of the fluid, we find the solution to the Wheeler-DeWitt equation on a mini-superspace. We solve this equation for a particular example of the initial wave function and analyze the evolution of the expectation value of the scale factor. We observe that the classical singularities disappear in the quantum model and a positive cosmological constant can describe an in ationary phase in the early universe and the current phase of accelerated expansion. We also study the in uence of arbitrary parameters of the initial wave function on the expectation value of the scale factor.