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arXiv 1508.03239gr-qcastro-ph.COhep-phhep-th
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圈量子宇宙学中的标量和张量扰动:高阶修正

Scalar and tensor perturbations in loop quantum cosmology: High-order corrections

Tao Zhu, Anzhong Wang, Gerald Cleaver, Klaus Kirsten, Qin Sheng, Qiang Wu

摘要:

圈量子宇宙学(LQC)为广义相对论暴胀模型中的反普朗克问题和初始奇点提供了有希望的解决方案。一般来说,由于量子化方法的不同,LQC涉及两种类型的量子校正,完整性和逆体积,对宇宙学背景演化和微扰。本文利用{ \em三阶一致渐近近似},在LQC的框架下,在这些量子修正下,明确地导出了慢卷暴胀的观测量.我们计算功率谱,谱指数,并运行的标量和张量扰动的谱指数,从而得到张量标量比。当暴胀模式穿过哈勃视界时,我们展开所有的观测量。由于三阶一致渐近逼近的误差上界为$\lesssim 0.15\%$,因此这些结果是迄今为止文献中得到的最精确的结果。它还表明,与逆体积校正,标量和张量谱表现出偏离通常的形状在大尺度。然后,利用普朗克,BAO和SN数据,我们得到了新的约束量子引力效应的LQC校正,并发现这种影响可能在即将到来的实验检测。

英文摘要:

Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {\em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $\lesssim 0.15\%$, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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