Quantum nature of Wigner function for inflationary tensor perturbations
arXiv:2002.01064 · doi:10.1007/JHEP03(2020)060
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.
arXiv comment(v1) 24 pages, (v2) 27 pages, discussions expanded and references added, to appear in Journal of High Energy Physics
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- Eternal inflation in light of Wheeler-DeWitt equation