Quantum nature of Wigner function for inflationary tensor perturbations

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.

(v1) 24 pages, (v2) 27 pages, discussions expanded and references added, to appear in Journal of High Energy Physics

References in corpus (5)

• The Effective Field Theory of Inflation
• Pointer states for primordial fluctuations in inflationary cosmology
• On the Decoherence of Primordial Fluctuations During Inflation
• Path Integral for Inflationary Perturbations
• Quantum non-linear evolution of inflationary tensor perturbations

Cited by in corpus (4)

• Quantum corrections to the primordial tensor spectrum: Open EFTs & Markovian decoupling of UV modes
• Boltzmann equations for astrophysical Stochastic Gravitational Wave Backgrounds scattering off of massive objects
• Instability of de Sitter space under thermal radiation in different vacua
• Eternal inflation in light of Wheeler-DeWitt equation