Abstract
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 αN and βN 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 αN and βN and their cross correlations contribute to the late-time field and conjugate momentum two-point functions. This happens both for light scalars \( \left(m<\frac{d}{2}H\right) \), corresponding to complementary series representations, and heavy scalars \( \left(m>\frac{d}{2}H\right) \), 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 βN autocorrelation contributes to the conjugate momentum two-point function in any dimensions and we gather hints that suggest αN to correspond to discrete series representations for this case at d = 3.
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Acknowledgments
We would like to sincerely thank Dionysios Anninos, Tarek Anous, Taha Ayfer, Armelle Bajat, Paolo Benincasa, Nicolas Boulanger, Alejandro Cabo-Bizet, Andrea Cavaglià, Claudia de Rham, Cem Eröncel, Atsushi Higuchi, Vasileios Letsios, Ben Pethybridge, Bayram Tekin, Ayngaran Thavanesan and Andrew Tolley for insightful discussions. GŞ acknowledges support by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 840709-SymAcc, from the European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (MSMT) (Project CoGraDS -CZ.02.1.01/0.0/0.0/15003/0000437) and from TÜBİTAK (The Scientific and Technological Research Council of Turkey) 2232 - B International Fellowship for Early Stage Researchers programme with project number 121C138 at different stages of this work. CS acknowledges support from the European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (MSMT) (Project CoGraDS - CZ.02.1.01/0.0/0.0/15003/0000437). We thank the anonymous referee for their helpful comments and GŞ thanks her newborn daughter and husband for creating the time to incorporate the revisions.
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Şengör, G., Skordis, C. Scalar two-point functions at the late-time boundary of de Sitter. J. High Energ. Phys. 2024, 76 (2024). https://doi.org/10.1007/JHEP02(2024)076
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DOI: https://doi.org/10.1007/JHEP02(2024)076