Quantum non-linear evolution of inflationary tensor perturbations. (English) Zbl 1416.83153
Summary: We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describes the quantum-to-classical transition of the tensor perturbations. This is different from the classicality accomplished by the squeezed state, the suppression of the non-commutative effect, which is originated from the quadratic, linear interaction, and also maintains the unitarity. The quantum-to-classical transition occurs within 5-10 \(e\)-folds, faster than the curvature perturbation.
MSC:
| 83F05 | Relativistic cosmology |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
Keywords:
cosmology of theories beyond the SM; effective field theories; quantum mechanical evolution; tensor perturbations during inflationReferences:
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