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arXiv 2110.01635hep-thastro-ph.COgr-qc
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德西特时空晚期边界上的标量两点函数

Scalar two-point functions at the late-time boundary of de Sitter

Gizem Sengor, Constantinos Skordis

备注：
The discussions on the massless scalar have been extended to include exceptional and discrete series invariant subspaces and inner products. An appendix with bulk calculations and confirmation that employing the late-time limit at the end or from the beginning leads to the same results have been included. This extended version is the version that will be submitted to a journal
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AI总结：

本文在一般维度德西特时空中用波函数图像和正则量子化两种方法计算标量场及其共轭动量的晚期边界两点函数，证明两种方法结果一致，并揭示了轻、重标量情形下 αN 与 βN 算符的自相关和互相关对两点函数的贡献机制。

摘要：

我们在一般 d+1 维时空中，采用 Bunch-Davies 边界条件，计算质量为 m 的标量场及其共轭动量在德西特时空晚期边界上的两点函数。我们分别使用波函数图像和正则量子化方法进行计算。通过后者可以清楚地看到，晚期场算符和共轭动量算符是归一化晚期算符 αN 和 βN 的线性组合，这些算符对应于具有良定义内积的德西特群的幺正不可约表示。这两种不同方法得到的两点函数相等，并且我们发现 αN 和 βN 的自相关以及它们的互相关都对晚期场和共轭动量的两点函数有贡献。这一结论既适用于轻标量（m<d/2 H），对应于德西特群的互补系列表示，也适用于重标量（m>d/2 H），对应于德西特群的主系列表示，其中 H 是德西特时空的哈勃尺度。在特殊情形 m=0 时，任意维度下只有 βN 的自相关对共轭动量两点函数有贡献，并且我们收集到的线索表明，在 d=3 时 αN 对应于离散系列表示。

英文摘要：

We calculate two-point functions of scalar fields of mass $m$ and their conjugate momenta at the late-time boundary of de Sitter with Bunch-Davies boundary conditions, in general $d+1$ spacetime dimensions. We perform the calculation using the wavefunction picture and using canonical quantization. With the latter one clearly sees how the late-time field and conjugate momentum operators are linear combinations of the normalized late-time operators $\alphaN$ and $\betaN$ that correspond to unitary irreducible representations of the de Sitter group with well-defined inner products. The two-point functions resulting from these two different methods are equal and we find that both the autocorrelations of $\alphaN$ and $\betaN$ and their cross correlations contribute to the late-time field and conjugate momentum two-point functions. This happens both for light scalars ($m<\frac{d}{2}H$), corresponding to complementary series representations, and heavy scalars ($m>\frac{d}{2}H$), corresponding to principal series representations of the de Sitter group, where $H$ is the Hubble scale of de Sitter. In the special case $m=0$, only the $\betaN$ autocorrelation contributes to the conjugate momentum two-point function in any dimensions and we gather hints that suggest $\alphaN$ to correspond to discrete series representations for this case at $d=3$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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