具有Brown-Kuchar尘埃的量子宇宙的么正演化
Unitary evolution of the quantum universe with a Brown-Kuchar dust
摘要：
本文用解析和数值方法研究了由Wheeler-DeWitt方程控制的空间平坦的Friedmann-Lemaitre-Robertson-Walker宇宙的波函数随时间的演化。为了在量子宇宙学中引入“时钟”，我们将Brown-Kuchar尘埃看作一个物质场，并采用Laplace-Beltrami算符序。哈密顿算子允许无穷多个自伴扩张，对应于minisuperspace中原点处的单参数边界条件族。对于边界条件中的任意扩张参数，波函数的演化都是幺正的，经典的初始奇异性被量子系统中的大反弹所取代。精确的波函数表明，宇宙空间体积的期望值在晚时服从经典时间演化，但方差发散。
英文摘要：
We study the time evolution of a wave function for the spatially flat Friedmann-Lemaitre-Robertson-Walker universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchar dust as a matter field in order to introduce a "clock" in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the universe obeys the classical time evolution in the late time but its variance diverges.
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