薛定谔型公式中的幂律展开宇宙学
Power-law expansion cosmology in Schrödinger-type formulation
摘要：
本文研究了非线性薛定谔型宇宙学，其中宇宙学系统是一个广义相对论FRLW宇宙，包含任意势下的正则标量场和具有任意空间曲率的正压流体.我们将该公式扩展到包括幻影场的情况，我们发现，薛定谔波函数在这个公式通常是不可归一化的。假设幂律展开，$a \sim t^q$，我们得到标量场势作为时间的函数。给出了薛定谔型公式中相应的薛定谔总能量、薛定谔势和波函数。
英文摘要：
We investigate non-linear Schrödinger-type formulation of cosmology of which our cosmological system is a general relativistic FRLW universe containing canonical scalar field under arbitrary potential and a barotropic fluid with arbitrary spatial curvatures. We extend the formulation to include phantom field case and we have found that Schrödinger wave function in this formulation is generally non-normalizable. Assuming power-law expansion, $a \sim t^q$, we obtain scalar field potential as function of time. The corresponding quantities in Schrödinger-type formulation such as Schrödinger total energy, Schrödinger potential and wave function are also presented.
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