标题： 拟线性演化补偿宇宙学扰动：非线性σ模型 显示英文标题

标题： Quasi-Linear Evolution of Compensated Cosmological Perturbations: The Nonlinear Sigma Model

摘要： 我们考虑来自“刚性源”的扰动在平坦FRW宇宙中的演化，例如在全局对称性破缺相变中形成的自序宇宙场，并通过Kibble机制演化。 尽管普通物质对源的线性响应取决于源动力学的细节，但我们证明，在短波长极限下，高阶非线性扰动方程会简化为与无源牛顿引力相同的形式。 因此，产生的$n$点相关函数及其谱对应项将具有由这种引力演化引起的层次贡献（如同无源情况），此外还可能来自非高斯初始条件的贡献。 我们将此形式应用于大$N$时的$O(N)$非线性σ模型，并发现，在大约$100\,h^{-1}{\rm Mpc}$波长以下的尺度上，预期不会出现与初始高斯扰动和牛顿引力在双谱和高阶相关性方面的可观测差异。 显示英文摘要

摘要： We consider the evolution of perturbations to a flat FRW universe that arise from a ``stiff source,'' such as a self-ordering cosmic field that forms in a global symmetry-breaking phase transition and evolves via the Kibble mechanism. Although the linear response of the normal matter to the source depends on the details of the source dynamics, we show that the higher-order non-linear perturbative equations reduce to a form identical to those of source-free Newtonian gravity in the small wavelength limit. Consequently, the resulting $n$-point correlation functions and their spectral counterparts will have a hierarchical contribution arising from this gravitational evolution (as in the source-free case) in addition to that possibly coming from non-Gaussian initial conditions. We apply this formalism to the $O(N)$ nonlinear sigma model at large $N$ and find that observable differences from the case of initially Gaussian perturbations and Newtonian gravity in the bispectrum and higher-order correlations are not expected on scales smaller than about $100\,h^{-1}{\rm Mpc}$.