Bispectrum from open inflation
Bispectrum from open inflation
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DOI：
10.1088/1475-7516/2013/11/065
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发表时间：
2013-09
影响因子：
6.4
通讯作者：
K. Sugimura;E. Komatsu
中科院分区：
文献类型：
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作者：
K. Sugimura;E. Komatsu
我们计算了在“开放暴胀”过程中产生的原初曲率扰动 z 的双谱。暴胀发生在通过量子隧道从背景假真空状态成核的气泡内部。我们的宇宙生活在气泡内，它可以被描述为具有负空间曲率的弗里德曼-勒马斯特-罗伯逊-沃克（FLRW）宇宙，正在经历慢速膨胀。我们特别关注量子涨落的初始态问题。由开放坐标绘制的德西特空间中的正频率模式定义的“真空状态”不同于欧几里得真空（相当于由平面坐标绘制的德西特空间中的正频率模式定义的所谓“邦奇-戴维斯真空”）。然后，量子隧道效应（气泡成核）将初始状态修改为远离原始的欧几里德真空。虽然之前大多数关于初始量子态修改的研究都是手工引入量子态修改的初始时间以及修改的形式，但在开放暴胀模型中，有效的初始时间自然会出现，并且形式是通过量子隧道效应固定的。因此，开放暴胀能够对修改后的初始状态对双谱的影响进行自洽计算。我们在所谓的压缩构型中找到了一个项，即 zk1zk2zk31/k12k34，k3 << k1 ≈ k2，这与之前关于初始状态修改的研究一致。精确折叠极限下的双谱，例如 k1 = k2+k3，也得到增强并保持有限。然而，当 ze 的波长小于宇宙的曲率半径时，这些项会呈指数抑制。前导双谱等于单场慢滚膨胀的通常双谱；当 ze 的波长小于曲率半径时，特定于开放暴胀的项仅出现在次领先阶中。
We calculate the bispectrum of primordial curvature perturbations, ζ, generated during ``open inflation.'' Inflation occurs inside a bubble nucleated via quantum tunneling from the background false vacuum state. Our universe lives inside the bubble, which can be described as a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) universe with negative spatial curvature, undergoing slow-roll inflation. We pay special attention to the issue of an initial state for quantum fluctuations. A ``vacuum state'' defined by a positive-frequency mode in de Sitter space charted by open coordinates is different from the Euclidean vacuum (which is equivalent to the so-called ``Bunch-Davies vacuum'' defined by a positive-frequency mode in de Sitter space charted by flat coordinates). Quantum tunneling (bubble nucleation) then modifies the initial state away from the original Euclidean vacuum. While most of the previous study on modifications of the initial quantum state introduces, by hand, an initial time at which the quantum state is modified as well as the form of the modification, an effective initial time naturally emerges and the form is fixed by quantum tunneling in open inflation models. Therefore, open inflation enables a self-consistent computation of the effect of a modified initial state on the bispectrum. We find a term which goes as ζk1ζk2ζk31/k12k34 in the so-called squeezed configurations, k3 << k1 ≈ k2, in agreement with the previous study on modifications of the initial state. The bispectrum in the exact folded limit, e.g., k1 = k2+k3, is also enhanced and remains finite. However, these terms are exponentially suppressed when the wavelength of ζ is smaller than the curvature radius of the universe. The leading-order bispectrum is equal to the usual one from single-field slow-roll inflation; the terms specific for open inflation arise only in the sub-leading order when the wavelength of ζ is smaller than the curvature radius.