摘要
Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.
Using the Hartle-Hawking method, we discuss the quantum Cosmology with O<sub>8N+1</sub><sup>-</sup>symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.
基金
Project supported by the National Natural Science Foundation of China.
