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Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory
Physical Review D ( IF 5 ) Pub Date : 2021-12-02 , DOI: 10.1103/physrevd.104.123510
Yu Han

In previous work, we showed that in loop quantum cosmology of scalar-tensor theory (STT) with the holonomy correction the background equations of motion in the Jordan frame have two branches, i.e., the b+ branch and the b branch. In the low-energy limit, the b+ branch of the equations of motion reproduce the equations of motion of classical STT, while the b branch of equations of motion do not reproduce the classical equations. In this paper, we investigate cosmological dynamics in an expanding universe whose background is described by the b branch of equations of motion of STT, and we especially focus on the dynamics of the perturbations in the low-energy limit because it is most relevant to the current observational range. First, we show that the low-energy limit of the b branch of equations of motion can be a stable attractor in the expansion phase of a universe. Then, we find a low-energy effective Hamiltonian on the spatially flat Friedmann-Robertson-Walker background. The background part of this Hamiltonian can yield the low-energy limit of the b branch of equations, and this Hamiltonian consists of constraints whose constraint algebra is different from the classical case but also closed up to arbitrary order of perturbations. Remarkably, we find that this Hamiltonian can be transformed into the Hamiltonian of the Einstein frame by field redefinitions different from the classical case. Moreover, we also develop the linear cosmological perturbation theory and apply it to study the slow-roll inflation in this context. Finally, we study a specific model of STT. In this model, a contracting universe described by classical STT in the remote past can pass through the bounce and evolve into an expanding universe whose background dynamics is described by the b branch of equations of motion. It is also shown that the slow-roll inflation can take place in this case, and the spectral indices of the slow-roll inflation agree well with the observations. The results in this paper indicate that there exists an alternative consistent theory which is different from the classical theory in the low-energy limit of loop quantum STT.

中文翻译:

圈量子标量张量理论低能极限下的非经典宇宙动力学

在之前的工作中,我们证明了在标量张量理论(STT)的环量子宇宙学中,带有完整校正的乔丹坐标系中的背景运动方程有两个分支,即 + 分行和 -分支。在低能极限下,+ 运动方程的分支再现了经典 STT 的运动方程,而 -运动方程的分支不能再现经典方程。在本文中,我们研究了膨胀宇宙中的宇宙动力学,其背景由-STT 运动方程的一个分支,我们特别关注低能量极限中扰动的动力学,因为它与当前的观测范围最相关。首先,我们证明了-运动方程的分支可以是宇宙膨胀阶段的稳定吸引子。然后,我们在空间平坦的 Friedmann-Robertson-Walker 背景上找到了一个低能量的有效哈密顿量。这个哈密顿量的背景部分可以产生低能量极限-方程的分支,并且这个哈密顿量由约束组成,其约束代数不同于经典情况,但也接近于任意阶的扰动。值得注意的是,我们发现这个哈密顿量可以通过不同于经典情况的场重定义转化为爱因斯坦坐标系的哈密顿量。此外,我们还开发了线性宇宙学微扰理论,并将其应用于在这种情况下研究慢滚膨胀。最后,我们研究了一个特定的 STT 模型。在这个模型中,在遥远的过去由经典 STT 描述的收缩宇宙可以通过反弹并演化成一个膨胀的宇宙,其背景动力学描述为-运动方程的分支。还表明在这种情况下可能会发生慢滚膨胀,并且慢滚膨胀的光谱指数与观测结果吻合良好。本文的研究结果表明,在环量子STT的低能极限上,存在一种不同于经典理论的替代一致性理论。
更新日期:2021-12-02
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