TY - JOUR

T1 - Probability of boundary conditions in quantum cosmology

AU - Suenobu, Hiroshi

AU - Nambu, Yasusada

N1 - Funding Information:
We would like to thank Meguru Komada for introducing us basic concept of Bayesian inference. YN was supported in part by JSPS KAKENHI Grant Numbers 15K05073 and 16H01094.
Publisher Copyright:
© 2017, Springer Science+Business Media New York.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. 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.

AB - 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. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. 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.

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U2 - 10.1007/s10714-017-2185-z

DO - 10.1007/s10714-017-2185-z

M3 - Article

AN - SCOPUS:85010002195

SN - 0001-7701

VL - 49

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

IS - 2

M1 - 19

ER -