Non-singular birth of the universe: High-performance numerical solutions of the Wheeler-DeWitt equation
G.A. Monerat (Departamento de Modelagem Computacional, Universidade do Estado do Rio de Janeiro, Instituto Politécnico, Rua Bonfim, 25, Vila Amélia, Nova Friburgo–RJ, CEP 28625-570, Brazil); H.J. Brumatto (Departamento de Engenharias e Computação, Universidade Estadual de Santa Cruz, Campus Soane Nazaré de Andrade, Rodovia Jorge Amado km 16, Bairro Salobrinho, Ilhéus–BA, CEP 45662-900, Brazil); G. Oliveira-Neto (Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora–MG, CEP 36036-330, Brazil)
; F.G. Alvarenga (Departamento de Física, Centro de Ciências Exatas, Universidade Federal do Espírito Santo, Avenida Fernando Ferrari 514, Goiabeiras, Vitória–ES, CEP 29075-910, Brazil); E.V. Corrêa Silva (Departamento de Matemática, Física e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Av. Dr. Omar Dibo Calixto Afrange s/n, Resende–RJ, CEP 27537-000, Brazil); et al - Show all 6 authors
Using high-performance computing, we obtain the wave function of a quantum cosmology model which aims at describing the early moments of the Universe. The model has a Friedmann-Robertson-Walker geometry with positive curvature of the spatial section, and its matter content consists of a massive scalar field conformally coupled to gravity, a radiation perfect fluid and a positive cosmological constant. The Wheeler-DeWitt equation of that model may be written in a form of a bi-dimensional Schrödinger equation with the presence of a potential barrier. After numerically solving this equation we let the wave function evolve until it reaches the potential barrier, either tunneling through or circumventing it. Using the many-worlds interpretation of quantum mechanics, we compute the expectation values of both the scale factor and the scalar field. If we consider that the present Universe was born after tunneling/circumventing the potential barrier, these results may provide a new perspective on the birth of the Universe and the fundamental processes that shaped its early evolution.