Abstract
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related to the explicit infrared divergence in the Wigner function, in contrast to the trace of the density matrix.
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ArXiv ePrint: 2002.01064
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Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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Gong, JO., Seo, MS. Quantum nature of Wigner function for inflationary tensor perturbations. J. High Energ. Phys. 2020, 60 (2020). https://doi.org/10.1007/JHEP03(2020)060
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DOI: https://doi.org/10.1007/JHEP03(2020)060