Bianchi型宇宙的量子化

QUANTIZATION OF THE BIANCHI TYPE UNIVERSE

本文将Ｗｈｅｅｌｅｒ—ＤｅＷｉｔｔ方程的平方根形式用于具有辐射场源的Ｂｉａｎｃｈｉ—Ⅰ型宇宙组成的微超空间模型，由此导出一个具有守恒流和正定几率密度的宇宙波函数．本文探讨了Ｂｉａｎｃｈｉ型宇宙的３次量子化，把类似于弯曲时空中量子场论程序应用到各向异性的Ｂｉａｎｃｈｉ—Ⅲ型宇宙中，给出了Ｗｈｅｅｌｅｒ—ＤｅＷｉｔｔ方程所满足的宇宙波函数解．把波函数作为微超空间中宇宙场算符看待后，不仅能解决量子宇宙学中几率解释的困难，而且也能得到宇宙多次产生的结论．同时估算了各种宇宙从“无”产生平均数目，给出了宇宙生成的分布，发现它遵从Ｐｌａｎｃｋ分布．

In this paper,We have used a square root formulation of the Wheeler-De Witt equation to quantize a minisuperspace model consisting of the Bianchi-I type universes with a radiation field source, Which leads to a wavefunction of the universe with a conserved current and a positive-definite probability density.We have also explored the third qualltization of the Bianch type universe.The procedure similar to an ordinary quantum field theory in curved space-time was applied to study the Bianchi-Ⅲ universe,We have given out the wave function solution satisfying Wheeler-De Witt equation.Based on regarding the wave function as the operator in a minisuperspace, not ohly the aifficulty in a probabilistic interpretation in the quantum cosmology have been circumvented,but also the conclusion of the multiple production of universe obtained. Furthemore we have estimated the average number of the prepuced universe from 'nothing', and have given the distribution of the produced universes, Which is planck distribution.