本论文包括三章. 在第一章, 我们简扼地回顾了圈量子引力理论(简称为LQG)的主要内容和主要方面. LQG是一种非微扰的量子引力理论, 将其应用到宇宙学中, 得到极早期宇宙演化的自洽图景, 经典奇性消失. LQG在宇宙学中的延伸和应用名为圈量子宇宙学(简称为LQC), 是我们所要关注的重点. 在介绍LQC之前, 我们先列出经典宇宙学的基本方程并详细阐述圈量子化的步骤, 然后引入修正经典方程的两种重要方法: 逆尺度因子修正和能量密度二次方修正. 这两种修正方法都起源于圈量子效应, 前者针对＃时(＃由简并参数j唯一决定)逆尺度因子的演化行为进行修正, 通过反弹消除大爆炸奇点, 并为暴胀发生的机制提供一种新的解释; 后者在本质上体现了时空几何量子离散性对于经典行为的影响. 第二章是我自己的研究工作. 我用哈密顿－雅科比方法求出了k = 0时逆尺度因子修正之下的两组宇宙学严格解, 它们都是反弹解, 并讨论其物理意义. 第三章是总结与展望.

This thesis contains three chapters. In the first chapter we present a brief review of loop quantum gravity (or LQG for short) on its main contents and main aspects. LQG is an attempt to quantize gravity non-perturbatively. When applied to cosmology, a consistent picture of the very early universe arises which is free of the classical singularities. We focus our attention on these applications which are named as loop quantumcosmology (LQC). Before studying LQC, we firstly list the basic equations of classical cosmology and introduce the procedure of loop quantization in detail. After that, two types of modifications to the Friedmann dynamics due to loop quantum effects are studied. First is based on the modification to the behavior of inverse scale factor below a critical scale factor # determined by an ambiguityparameter j. Inverse scale factor modification causes a bounce and remove the big bang singularity, it can also provide a new mechanism for the occurrence of inflation. The seconed type which is called # modification essentially encodes the discrete quantum geometric nature of spacetime. The second chapter is as my own work. The Hamilton-Jacobi method for getting exact solutions is constructed and two sets of bouncing solutions areobtained, afterwards we discuss their physical meanings. Finally, in the third chapter, we review briefly the history of cosmology and give some outlooks.