标题： 关于原初可观测量中的发散正则化和重整化的研究 显示英文标题

标题： An Étude on the Regularization and Renormalization of Divergences in Primordial Observables

摘要： 许多感兴趣的宇宙学可观测量来源于早期真空涨落演化至晚期的结果。 这些可观测量代表了从某些基本的量子场论或统计场论框架中得出的统计抽样，其中会出现无穷大并需要正规化处理。 在去除发散项后，必须通过某个尺度上的测量或观测施加重整化条件，同时注意方案和背景依赖性。 我们回顾了在从有限持续膨胀过渡到辐射主导的背景下这一过程，并展示了尽管无量纲积分普遍存在，但紫外发散仍能从名义上归零的量中被有意义地提取出来。 通过这种方式，可以将具有硬截止的计算上下文化，区分与膨胀开始和结束对应的紫外和红外尺度，以及与理论及其可观测物未知完成对应的紫外和红外尺度。 这种区分具有重要意义，因为可观测量不能依赖于后者，尽管它们肯定会依赖于前者。 还可以明确展示紫外发散对数系数的方案无关性。 此外，某些红外发散可以被视为 de Sitter 极限的产物，在有限持续膨胀下可以得到治愈。 对于引力波可观测量，我们强调需要正规化那些在构建过程中没有预先假设尺度分离的应力张量（如同标准的 Isaacson 形式），并推导出适合特定目的的改进应力张量。 最后，我们强调了从真空张量扰动推断$N_{\rm eff}$边界与背景重整化过程之间密不可分的联系。 显示英文摘要

摘要： Many cosmological observables of interest derive from primordial vacuum fluctuations evolved to late times. These observables represent statistical draws from some underlying quantum or statistical field theoretic framework where infinities arise and require regularization. After subtracting divergences, renormalization conditions must be imposed by measurements or observations at some scale, mindful of scheme and background dependence. We review this process on backgrounds that transition from finite duration inflation to radiation domination, and show how in spite of the ubiquity of scaleless integrals, UV divergences can still be meaningfully extracted from quantities that nominally vanish when dimensionally regularized. In this way, one can contextualize calculations with hard cutoffs, distinguishing between UV and IR scales corresponding to the beginning and end of inflation from UV and IR scales corresponding the unknown completion of the theory and its observables. This distinction has significance as observable quantities cannot depend on the latter although they will certainly depend on the former. One can also explicitly show the scheme independence of the coefficients of UV divergent logarithms. Furthermore, certain IR divergences can be shown to be an artifact of the de Sitter limit and are cured for finite duration inflation. For gravitational wave observables, we stress the need to regularize stress tensors that do not presume a prior scale separation in their construction (as with the standard Isaacson form), deriving an improved stress tensor fit to purpose. We conclude by highlighting the inextricable connection between inferring $N_{\rm eff}$ bounds from vacuum tensor perturbations and the process of background renormalization.