Abstract
Positivity bounds represent nontrivial limitations on effective field theories (EFTs) if those EFTs are to be completed into a Lorentz-invariant, causal, local, and unitary framework. While such positivity bounds have been applied in a wide array of physical contexts to obtain useful constraints, their application to inflationary EFTs is subtle since Lorentz invariance is spontaneously broken during cosmic inflation. One path forward is to employ a Breit parameterization to ensure a crossing-symmetric and analytic S-matrix in theories with broken boosts. We extend this approach to a theory with multiple fields, and uncover a fundamental obstruction that arises unless all fields obey a dispersion relation that is approximately lightlike. We then apply the formalism to various classes of inflationary EFTs, with and without isocurvature perturbations, and employ this parameterization to derive new positivity bounds on such EFTs. For multifield inflation, we also consider bounds originating from the generalized optical theorem and demonstrate how these can give rise to stronger constraints on EFTs compared to constraints from traditional elastic positivity bounds alone. We compute various shapes of non-Gaussianity (NG), involving both adiabatic and isocurvature perturbations, and show how the observational parameter space controlling the strength of NG can be constrained by our bounds.
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Acknowledgments
We thank Simone Ferraro, Daniel Green, and Scott Melville for useful discussions and comments. M.F. is supported by the U.S. Department of Energy (DOE) under grant DE-SC0010008. S.K. is supported in part by the U.S. National Science Foundation (NSF) grant PHY-1915314 and the DOE contract DE-AC02-05CH11231. M.F. & S.K. thank the Mainz Institute of Theoretical Physics of the Cluster of Excellence PRISMA+ (Project ID 39083149) for its hospitality while this work was in progress. M.F. also thanks the Aspen Center for Physics, supported by NSF grant PHY-1607611, for its hospitality while this work was in progress. G.N.R. is supported at the Kavli Institute for Theoretical Physics by the Simons Foundation (Grant No. 216179) and the NSF (Grant No. PHY-1748958) and at the University of California, Santa Barbara by the Fundamental Physics Fellowship.
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Freytsis, M., Kumar, S., Remmen, G.N. et al. Multifield positivity bounds for inflation. J. High Energ. Phys. 2023, 41 (2023). https://doi.org/10.1007/JHEP09(2023)041
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DOI: https://doi.org/10.1007/JHEP09(2023)041