arXiv 2007.038662020-07hep-thastro-ph.COgr-qchep-ph

基于Wheeler-DeWitt方程的永恒暴涨

Eternal inflation in light of Wheeler-DeWitt equation

Min-Seok Seo

备注：: 22 pages, version published in JCAP
发表信息：: JCAP 11 (2020) 007
DOI：: 10.1088/1475-7516/2020/11/007

摘要：

惠勒-德威特方程提供了暴胀子的曲率扰动和规范不变量子涨落的概率分布。由此，我们可以找到一个塔的功率谱，这是没有发现在微扰的方法。由于穿过视界的模的功率谱对经典暴胀子位移的不确定性有贡献，我们得到了永恒暴胀的新条件。在补丁的存在下，在更高的激发，慢滚参数上的限制允许永恒的通货膨胀是由最多$ε\lesssim (2n+1)(H/m_{\rm Pl})^2$与$n$整数表示的量子数标记的激发。对于大的$n$，放松对$ε$的约束，使得可以用更大的$ε$值发生永恒的暴胀。虽然热力学第二定律意味着$n=0$态是优选的，但是我们不能忽略这样大的$n$效应，因为诱导跃迁到$n=0$态的非线性相互作用被抑制。

英文摘要：

The Wheeler-DeWitt equation provides the probability distribution for the curvature perturbation, the gauge invariant quantum fluctuation of the inflaton. From this, we can find a tower of power spectra which is not found in a perturbative approach. Since the power spectrum for the modes that cross the horizon contributes to the uncertainty in the classical inflaton displacement, we obtain new conditions for eternal inflation. In the presence of the patch in the higher excitations, the bound on the slow-roll parameter allowing eternal inflation is given by at most $ε\lesssim (2n+1)(H/m_{\rm Pl})^2$ with $n$ integer indicating the quantum number labelling the excitation. For large $n$, the bound on $ε$ is relaxed such that eternal inflation can take place with even larger value of $ε$. While the second law of thermodynamics implies that $n=0$ state is preferred, we cannot ignore such large $n$ effect since the nonlinear interaction inducing transitions to the $n=0$ state is suppressed.

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