摘要
本文在Ｂｉａｎｃｈｉ－Ⅲ时空流形中，研究了具有正的宇宙常数的Ｅｉｎｓｔｅｉｎ引力论在微超空间模型中的Ｖｉｌｅｎｋｉｎ边界条件提案．借助于局域坐标和延迟函数的特殊选择，经典运动方程简化为闵氏时空中自由粒子的运动方程．采用正则量子化途径得到了Ｗｈｅｅｌｅｒ－ＤｅＷｉｔ方程，并且发现它类似于均匀的和各向同性的宇宙模型中的情况．利用同样的局域坐标，Ｗｈｅｅｌｅｒ－ＤｅＷｉｔ方程可化为类似于具有一个负质量项的Ｋｌｅｉｎ－Ｇｏｒｄｏｎ方程．在Ｖｉｌｅｎｋｉｎ提案下得到了单参数类和双参数类的波函数，而且发现这个提案仅限定了解的集合，但不能唯一地确定宇宙的波函数．
In this paper,the boundary condition of initial universe proposed by Vilenkin was studied for the Einstein`s theory of gravitation with a positive cosmological contant in the minisuperspace model based on the Bianchi Ⅲ manifold.The classical equations of motion can be reduced to the motion equations of free particle in the Minkowskin spacetime by the Special choose of local coordinate and lapse function.The Wheeler-DeWitt equation was obtioned in terms of the canonical quantization approach,which is equivalent to that in the homogeneous and isotropic model of universe.The Wheeler-DeWitt equation is also similar to the Klein-Gordon equation with a negative massive term by using the same local coordinate. We derived the single parameter and double parameter wave function by means of Vilenkin proposal. We also found that this proposal just confined the set of solutions but could not determine solely the wave function of universe.
