Scalar two-point functions at the late-time boundary of de Sitter
| Autor: | Sengor, Gizem, Skordis, Constantinos |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $d=3$. Comment: 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 |
| Databáze: | arXiv |
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