Cosmology from random multifield potentials
Cosmology from random multifield potentials
复制标题
随机多场势的宇宙学
DOI：
10.1088/1475-7516/2006/03/013
复制
发表时间：
2005
影响因子：
6.4
通讯作者：
R. Easther
中科院分区：
文献类型：
--
作者：
A. Aazami;R. Easther
我们考虑与随机多场势相关的真空和膨胀轨迹的统计性质。我们的潜在动机是弦景观，但我们的计算适用于一般势。利用随机矩阵理论，我们分析了与该势的极值有关的海森矩阵。这些势一般有大量的极值。我们证明了，如果交叉耦合(非对角线项)与自耦合(对角线项)同阶，则所有极值本质上都是鞍点，且极小值的个数实际上为零。要避免这一点，需要相同的尺度分离，以确保牛顿常数在弦线景观中相对于辐射修正是稳定的。利用中心极限定理，我们发现，即使极值的数量是巨大的，极值之间的典型距离仍然是巨大的-这对依赖于景观中复杂路径的存在的通货膨胀模型具有挑战性。
We consider the statistical properties of vacua and inflationary trajectories associated with a random multifield potential. Our underlying motivation is the string landscape, but our calculations apply to general potentials. Using random matrix theory, we analyse the Hessian matrices associated with the extrema of this potential. These potentials generically have a vast number of extrema. We show that if the cross-couplings (off-diagonal terms) are of the same order as the self-couplings (diagonal terms), essentially all extrema are saddles, and the number of minima is effectively zero. Avoiding this requires the same separation of scales as is needed to ensure that Newton’s constant is stable against radiative corrections in a string landscape. Using the central limit theorem we find that even if the number of extrema is enormous, the typical distance between extrema is still substantial—with challenging implications for inflationary models that depend on the existence of a complicated path inside the landscape.