标题： 量化歧义与圈量子宇宙学中标量-张量理论的有效动力学 显示英文标题

标题： Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology

摘要： 标量-张量理论在乔丹框架下的哈密顿约束在环量子宇宙学中使用三种量化方案进行量化，由此得到三种不同的有效哈密顿约束。 从这些有效哈密顿约束导出的相应运动方程结果差异很大。 详细讨论了每组有效运动方程的含义。 在本文的后半部分，作为具体例子，我们研究了一个具有非最小耦合函数$F(\phi)=1+\xi\kappa\phi^2$和自相互作用四次势的特定模型的有效动力学。 通过数值结果，我们发现了不同有效动力学的不同特征。 此外，还发现该模型的每种有效动力学中都不存在时空奇点，并且存在宇宙反弹。 显示英文摘要

摘要： The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The corresponding effective equations of motion derived from these effective Hamiltonian constraints turn out to be drastically different. The implications of each set of effective equations of motion are discussed in detail. In the latter half of this paper, as a concrete example, we study the effective dynamics of a specific model with the non-minimal coupling function $F(\phi)=1+\xi\kappa\phi^2$ and self-interacting quartic potential. Using numerical results, we find different features for different effective dynamics. Moreover, it is also found that the spacetime singularity is absent and the cosmological bounce exists in each effective dynamics of this model.