标题： 闭宇宙中的密度扰动和原初非高斯性 显示英文标题

标题： Density Perturbations and Primordial Non-Gaussianities in a Closed Universe

摘要： 宇宙的空间曲率尚不清楚。 尽管目前宇宙非常接近于基本上是平直的，且曲率的大部分特征似乎已经被暴胀所稀释，但如果暴胀期间的e-foldings数量接近于解释视界问题所需的最小值，那么宇宙的曲率可能在宇宙微波背景（CMB）中留下了可观察的痕迹，尤其是在大角度处。 受量子宇宙学一般结果的启发，并利用有效场论技术，我们开发了一种通用方法，用于解析计算闭合宇宙中密度扰动的功率谱。 遵循哈密顿形式主义，我们确定了相应的Bunch-Davis真空，找到了两点函数和高阶关联函数的解析表达式，展开为$S^3$拉普拉斯球谐函数。 特别是我们关注对可观测非高斯性的潜在影响。 我们考虑三次相互作用以及更高阶导数项，以探讨声速$c_s\neq 1$的后果。 对于大多重极，曲率效应可以忽略不计，并重现平坦情况下的已知结果。 然而，在相对较小的多重极情况下，它们偏离了平坦空间的结果。 在这种极限下，非高斯性可能导致潜在可观测的$f_{\rm NL}$值。 特别是我们在$f_{\rm NL}$中发现了平坦空间情况下不存在的项，这些项在大尺度上很重要，即使长时间的暴胀稀释了曲率，也可能被观测到。 我们将我们的结果与文献中的先前讨论进行了比较。 显示英文摘要

摘要： The spatial curvature of the universe is not yet known. Even though at present the Universe is very close to being essentially flat and most signatures of curvature appear to have been diluted by inflation, if the number of e-foldings during inflation is close to the minimum necessary to explain the horizon problem, the curvature of the universe may have left imprints in the cosmic microwave background (CMB) that may be observable, especially at large angles. Motivated by general results on quantum cosmology and using effective field theory techniques, we develop a general approach for analytically computing the power spectrum of density perturbations for a closed universe. Following a Hamiltonian formalism we determine the corresponding Bunch-Davis vacuum, find analytic expressions for two-point functions and higher correlators, expanding in terms of $S^3$ harmonics. In particular we concentrate on potential implications for observable non-Gaussianities. We consider cubic interactions as well as higher derivative ones to explore the consequence of a speed of sound $c_s\neq 1$. For large multipoles curvature effects are negligible and reproduce the known results for the flat case. However, they depart from the flat space result for relatively small multipoles. In this limit non-Gaussianities may lead to potentially observable values of $f_{\rm NL}$. In particular we find terms in $f_{\rm NL}$ that are absent in the flat space case, which are important at large scales and may be observable even if a long period of inflation dilutes the curvature. We compare our results with previous discussions in the literature.