量子修正弗里德曼方程  

Quantum Modified Friedmann Equations

作　　者：何东山 蔡庆宇 HE Dongshan;CAI Qingyu(School of Physics&Electronic Engineering,Xianyang Normal University,Xianyang 712000,Shaanxi,China;State Key Laboratory of Magnetic Resonances and Atomic and Molecular Physics,Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,Hubei,China)

机构地区：[1]咸阳师范学院物理与电子工程学院,陕西咸阳712000 [2]中国科学院物理与数学研究所,波谱与原子分子国家重点实验室,湖北武汉430071

出　　处：《咸阳师范学院学报》2021年第2期1-5,共5页Journal of Xianyang Normal University

基　　金：国家杰出青年科学基金项目(11725524);陕西省高校青年杰出人才支持计划;陕西省自然科学基金项目(2019JQ-900);咸阳师范学院骨干教师项目(XSYGG201802)。

摘　　要：从量子宇宙学基本方程惠勒-德维特方程出发,结合玻姆轨道理论给出了描述宇宙量子效应的量子势以及弗里德曼方程的量子修正。量子修正弗里德曼方程表明宇宙尺度因子的演化受到经典势与量子势的共同影响。通过求解量子修正弗里德曼方程,证明极早期宇宙中量子效应显著,宇宙的量子效应推动了宇宙暴涨并且使早期宇宙避免了大爆炸奇点。随着宇宙的长大,量子效应减弱,量子修正弗里德曼方程过渡到经典弗里德曼方程。From Wheeler-DeWitt equation, the fundamental equation of quantum cosmology, together with the de Broglie-Bohm quantum trajectory theory, we derive the cosmological quantum potential and quantum modified Friedmann equations. Quantum modified Friedman equations contain a pair of quantum potential terms: quantum potential and classical potential, which determines the evolution of the universe scale facor. Then, by solving quantum modified Friedman equations, it is shown that quantum potential is important in early universe, and that it provides the power of the inflation and makes the universe avoid the big-bang singularity. However, with the expansion of the universe, and the rapid decrease of the quantum potential, the quantum modified Friedman equations shift to the classical Friedman equations.

关 键 词：量子势 弗里德曼方程 暴涨 量子宇宙学 

分 类 号：O412.1[理学—理论物理]