论文标题
宇宙学扰动的重新归一化组和紫外线完成：重力崩溃是一种关键现象
Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon
论文作者
论文摘要
众所周知，宇宙学的扰动理论因预测球形崩溃和无碰撞物质的空隙演变而融合不佳。使用确切的参数溶液作为测试地面，我们在球形对称性中开发了两种渐近方法，这些方法将重力演化的精度远高于拉格朗日扰动理论（LPT），这是文献中当前的金标准。其中一种方法选择了稳定的重新分组流程方程的定点解决方案，从而在领先顺序上已经预测了相位过渡到折叠结构的关键指数。另一种方法通过添加一个非分析术语来捕获重力崩溃的临界性质，从而使截短的LPT系列远离了UV状态。我们发现，紫外线方法最准确地解析了非线性密度及其单点概率分布函数的演变。同样，通过重新归一化组方法可以实现准确的预测，尤其是与Padé近似值配对时。此外，我们的结果产生了新的，非常准确的公式，以相关线性和非线性密度对比。最后，我们绘制了如何使方法适应宇宙随机场初始条件的情况。
Cosmological perturbation theory is known to converge poorly for predicting the spherical collapse and void evolution of collisionless matter. Using the exact parametric solution as a testing ground, we develop two asymptotic methods in spherical symmetry that resolve the gravitational evolution to much higher accuracy than Lagrangian perturbation theory (LPT), which is the current gold standard in the literature. One of the methods selects a stable fixed-point solution of the renormalization-group flow equation, thereby predicting already at the leading order the critical exponent of the phase transition to collapsed structures. The other method completes the truncated LPT series far into the UV regime, by adding a non-analytic term that captures the critical nature of the gravitational collapse. We find that the UV method most accurately resolves the evolution of the nonlinear density as well as its one-point probability distribution function. Similarly accurate predictions are achieved with the renormalization-group method, especially when paired with Padé approximants. Further, our results yield new, very accurate, formulas to relate linear and nonlinear density contrasts. Finally, we chart possible ways on how to adapt our methods to the case of cosmological random field initial conditions.
