通过模式匹配调节红外：恒定减速膨胀空间中的无质量标量
Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration
摘要：
本文考虑了在$D$维FLRW时空中的无质量标量场，其中$ξ$与Ricci标量可能存在耦合，且$q=ε-1$，$ε=-{\dot{H}}/{H^2}$为常减速参数.这种理论的Bunch-Davies真空的关联函数早就被认为是在$ε$的宽范围内红外发散的。我们解决这些分歧，明确匹配的时空在考虑没有红外发散的时空。这样的过程确保了与感兴趣时空中的真空相关的所有关联函数都是红外有限的。在这个新定义的真空中，我们构造了传播子的重合极限，并作为例子计算了应力能张量的期望值。我们发现，这种方法在紫外和红外两个令人满意的结果。此外，我们发现，除非由于耦合到里奇标量$ξR$的有效质量是负的，量子贡献的能量密度总是稀释更快，或一样快，作为背景能量密度。因此，量子逆反应在一个环阶上是无关紧要的，除非$ξR$是负的。最后，我们将这种方法与已知的结果进行比较，其中红外线是通过将宇宙放在一个有限的盒子中来调节的。在一个加速的宇宙中，结果在性质上是相同的，只要在匹配时用物理哈勃半径来确定宇宙的大小。然而，在一个减速的宇宙中，这两种方案给出了不同的量子应力能量张量的后期行为。这是因为在这种情况下，调节红外线的长度尺度在后期变成了亚哈勃。
英文摘要：
In this paper we consider a massless scalar field, with a possible coupling $ξ$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constant deceleration parameter $q=ε-1$, $ε=-{\dot{H}}/{H^2}$. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of $ε$. We resolve these divergences by explicitly matching the spacetime under consideration to a spacetime without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the spacetime of interest are infrared finite. In this newly defined vacuum we construct the coincidence limit of the propagator and as an example calculate the expectation value of the stress energy tensor. We find that this approach gives both in the ultraviolet and in the infrared satisfactory results. Moreover, we find that, unless the effective mass due to the coupling to the Ricci scalar $ξR$ is negative, quantum contributions to the energy density always dilute away faster, or just as fast, as the background energy density. Therefore, quantum backreaction is insignificant at the one loop order, unless $ξR$ is negative. Finally we compare this approach with known results where the infrared is regulated by placing the Universe in a finite box. In an accelerating universe, the results are qualitatively the same, provided one identifies the size of the Universe with the physical Hubble radius at the time of the matching. In a decelerating universe however, the two schemes give different late time behavior for the quantum stress energy tensor. This happens because in this case the length scale at which one regulates the infrared becomes sub-Hubble at late times.
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