Non-Gaussianity in Two-Field Inflation
Non-Gaussianity in Two-Field Inflation
复制标题
两场暴胀中的非高斯性
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Max Tegmark
中科院分区：
文献类型：
--
作者：
C. Peterson;Max Tegmark
我们推导出一般双场暴胀中局部双谱和三谱的半解析公式，并为建立具有可观测非高斯性的观测允许模型提供了一个简单的几何配方。我们使用\delta N形式主义和传递函数形式主义来表示双谱几乎完全在模型无关的物理量。类似地，我们计算了三谱，并表明三谱参数\τ NL可以完全用谱观测量来表示，这提供了一个新的一致性关系，这是双场暴胀所独有的。我们表明，为了在通货膨胀期间产生可观的大的非高斯性，曲率模式的等曲率模式的来源必须是非常敏感的初始条件，以及采购量必须是适度的，以避免过度微调。在一些最小的假设下，我们认为，只有当相邻的轨道通过二维场空间在通货膨胀期间发散时，第一个条件才得到满足。从几何学上讲，这意味着暴胀子在暴胀过程中必须沿着势V中的一个脊滚动一段时间，并且它的轨迹必须在场空间中稍微转弯（但不要太急）。因此，它遵循两个领域的情况下，吸引子解决方案必然会产生小的非高斯性。这就解释了为什么在双场暴胀中很难实现大的非高斯性，以及为什么它只在一小类模型中实现，比如混合暴胀和某些乘积势，其中势和/或初始条件被微调。我们的一些结论定性地推广到一般的多场暴胀。
We derive semi-analytic formulae for the local bispectrum and trispectrum in general two-field inflation and provide a simple geometric recipe for building observationally allowed models with observable non-Gaussianity. We use the \delta N formalism and the transfer function formalism to express the bispectrum almost entirely in terms of model-independent physical quantities. Similarly, we calculate the trispectrum and show that the trispectrum parameter \tau NL can be expressed entirely in terms of spectral observables, which provides a new consistency relation unique to two-field inflation. We show that in order to generate observably large non-Gaussianity during inflation, the sourcing of curvature modes by isocurvature modes must be extremely sensitive to the initial conditions, and that the amount of sourcing must be moderate in order to avoid excessive fine-tuning. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories through the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn slightly (but not too sharply) in field space. Therefore, it follows that two-field scenarios with attractor solutions necessarily produce small non-Gaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation, and why it has only been achieved in a narrow class of models like hybrid inflation and certain product potentials where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize qualitatively to general multi-field inflation.
影响因子：
8.7
作者：
Komatsu, E.;Smith, K. M.;Wright, E. L.
通讯作者：
Wright, E. L.