标题： 通过模式匹配调节红外：具有恒定减速度的扩展空间中的无质量标量 显示英文标题

标题： Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration

摘要： 在本文中，我们考虑一个无质量的标量场，在具有常数减速度参数$q=\epsilon-1$，$\epsilon=-{\dot{H}}/{H^2}$的$D$维 FLRW 时空下，可能与 Ricci 标量$\xi$相耦合。 这种理论的 Bunch-Davies 真空的相关函数长期以来已知对于$\epsilon$的广泛取值范围是红外发散的。 我们通过显式地将所考虑的时空与没有红外发散的时空进行匹配来解决这些发散问题。 这种程序确保了相对于感兴趣时空中的真空的所有相关函数都是红外有限的。 在这个新定义的真空中，我们构造传播子的重合极限，并作为例子计算应力能量张量的期望值。 我们发现这种方法在紫外和红外区域都给出了满意的结果。 此外，我们发现除非由于与 Ricci 标量$\xi R$耦合产生的有效质量为负，否则量子对能量密度的贡献总是比背景能量密度稀释得更快或同样快。 因此，在一环阶次下，除非$\xi R$为负，量子反作用是不重要的。 最后，我们将这种方法与已知的结果进行比较，其中通过将宇宙置于有限盒子中来调节红外发散。 在加速宇宙中，结果定性相同，只要将宇宙的大小与匹配时刻的物理哈勃半径相联系。 然而在减速宇宙中，这两种方案对于量子应力能量张量的晚期行为给出了不同的结果。 这是因为在这种情况下，调节红外的长度尺度在晚期变得小于哈勃尺度。 显示英文摘要

摘要： In this paper we consider a massless scalar field, with a possible coupling $\xi$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constant deceleration parameter $q=\epsilon-1$, $\epsilon=-{\dot{H}}/{H^2}$. 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 $\epsilon$. 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 $\xi R$ 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 $\xi R$ 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.