Probability of boundary conditions in quantum cosmology

[摘要] One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.

[发布机构] Department of Physics, Graduate School of Science, Nagoya University, Chikusa, Nagoya; 464-8602, Japan^1;Mitsubishi Electric Corporation Information Technology R and D Center, Japan^2

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Cosmological constants;Exact solution;Foldings;Model parameters;Observational data;Quantum cosmology;Scalar fields;Wheeler-De Witt equation