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arXiv 1005.3307hep-thastro-ph.CO
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暴胀红外发散:再加热面的几何形状与Δ N形式

Inflationary Infrared Divergences: Geometry of the Reheating Surface vs. delta N Formalism

Christian T. Byrnes, Mischa Gerstenlauer, Arthur Hebecker, Sami Nurmi, Gianmassimo Tasinato

摘要:

我们描述了一个简单的方法,将波动的哈勃尺度在视界出口的标量扰动到三角洲N形式主义。主要的影响来自哈勃尺度对暴胀子低频模式的依赖。这修改了出现在曲率谱中的对数增强项的系数在二阶场波动。通过这种修改,相关系数与树级谱相对于视界出口处暴胀子φ的二阶导数成比例。具有精确相同系数的对数出现在纯粹基于再加热表面的几何形状的曲率谱的对数增强的计算中。我们认为这一协议是对拟议实施的Δ N形式主义的有力支持。此外,我们的分析表明,如果暴胀功率谱的对数增强是用再加热表面(或任何其他恒定能量密度的暴胀后表面)上的全局坐标系定义的,那么这个量确实是物理性的。然而,它可以通过在该表面上使用不变距离定义光谱来避免。

英文摘要:

We describe a simple way of incorporating fluctuations of the Hubble scale during the horizon exit of scalar perturbations into the delta N formalism. The dominant effect comes from the dependence of the Hubble scale on low-frequency modes of the inflaton. This modifies the coefficient of the log-enhanced term appearing in the curvature spectrum at second order in field fluctuations. With this modification, the relevant coefficient turns out to be proportional to the second derivative of the tree-level spectrum with respect to the inflaton phi at horizon exit. A logarithm with precisely the same coefficient appears in a calculation of the log-enhancement of the curvature spectrum based purely on the geometry of the reheating surface. We take this agreement as strong support for the proposed implementation of the delta N formalism. Moreover, our analysis makes it apparent that the log-enhancement of the inflationary power-spectrum is indeed physical if this quantity is defined using a global coordinate system on the reheating surface (or any other post-inflationary surface of constant energy density). However, it can be avoided by defining the spectrum using invariant distances on this surface.

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