Quantum nature of Wigner function for inflationary tensor perturbations

Jinn Ouk Gong, Min Seok Seo

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3 Scopus citations


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.

Original languageEnglish
Article number60
JournalJournal of High Energy Physics
Issue number3
StatePublished - 1 Mar 2020

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© 2020, The Author(s).


  • Cosmology of Theories beyond the SM
  • Effective Field Theories


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