2012/06/21 by Oliveira-Neto, G., Monerat, G. A., Silva, E. V. Corrêa +2
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.1206.5029
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant curvatures. We work in the Schutz's variational formalism. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded. Therefore, we compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter (θ). The solutions to the Wheeler-DeWitt equation are function of the scale factor (a) and a time variable (τ), associated to the fluid. They also depend on an integer (n) and θ. The most general solution (Ψ(a,τ)) to the Wheeler-DeWitt equation is a sum, in the integer n, of the solutions mentioned above. We observe that, there is no Ψ(a,τ) satisfying the appropriate boundary conditions. Therefore, we conclude that it is not possible to obtain a wavefunction satisfying the appropriate boundary conditions for the present model with the considered noncommutativity.