Abstract
Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of particular oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.
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Acknowledgments
We are grateful to Tim Cohen, Yi Guo, Jiashu Han, Akhil Premkumar, Kamran Salehi Vaziri and Ben Wallisch for helpful discussions. We also thank Tim Cohen for comments on the draft. DB is supported by a VIDI grant of the Netherlands Organization for Scientific Research (NWO) and a Yushan Professorship at National Taiwan University (NTU) funded by the Ministry of Education (MOE), Taiwan. DG and YH are supported by the US Department of Energy under grant DE-SC0009919. CHS is supported by the Ministry of Education, Taiwan (MOE Yushan Young Scholar grant NTU-112V1039).
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Green, D., Huang, Y., Shen, CH. et al. Positivity from Cosmological Correlators. J. High Energ. Phys. 2024, 34 (2024). https://doi.org/10.1007/JHEP04(2024)034
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DOI: https://doi.org/10.1007/JHEP04(2024)034