Abstract
Massive fields can imprint unique oscillatory features on primordial correlation functions or inflationary correlators, which is dubbed the cosmological collider signal. In this work, we analytically investigate the effects of a time-dependent mass of a scalar field on inflationary correlators, extending previous numerical studies and implementing techniques developed in the cosmological bootstrap program. The time-dependent mass is in general induced by couplings to the slow-roll inflaton background, with particularly significant effects in the case of non-derivative couplings. By linearly approximating the time dependence, the mode function of the massive scalar is computed analytically, on which we derive analytic formulae for two-, three-, and four-point correlators with the tree-level exchange of the massive scalar. The obtained formulae are utilized to discuss the phenomenological impacts on the power spectrum and bispectrum, and it is found that the scaling behavior of the bispectrum in the squeezed configuration, i.e., the cosmological collider signal, is modified from a time-dependent Boltzmann suppression. By investigating the scaling behavior in detail, we are in principle able to determine the non-derivative couplings between the inflaton and the massive particle.
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Acknowledgments
We thank Lucas Pinol, Yi Wang and Zhong-Zhi Xianyu for valuable discussions and their hospitalities when F.S. stayed at their groups, Dong-Gang Wang and Sebastien Renaux-Petel for valuable discussions in Gravity 2023, YITP and COSMO 2023, IFT, and Yuhang Zhu for valuable discussions. S.A. is supported by IBS under the project code, IBS-R018-D1. T.N. is supported in part by JSPS KAKENHI Grant No. 20H01902 and No. 22H01220, and MEXT KAKENHI Grant No. 21H05184 and No. 23H04007. F.S. is supported by financial aid from the Center for the Theoretical Physics of the Universe, Institute for Basic Science, financial aid from the Advanced Research Center for Quantum Physics and Nanoscience, Tokyo Institute of Technology, and JSPS Grant-in-Aid for Scientific Research No. 23KJ0938. M.Y. is supported by IBS under the project code IBS-R018-D3 and JSPS Grant-in-Aid for Scientific Research No. JP21H01080.
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Aoki, S., Noumi, T., Sano, F. et al. Analytic formulae for inflationary correlators with dynamical mass. J. High Energ. Phys. 2024, 73 (2024). https://doi.org/10.1007/JHEP03(2024)073
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DOI: https://doi.org/10.1007/JHEP03(2024)073