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Confronting the trans-Planckian question of inflationary cosmology with dissipative effects. (English) Zbl 1145.83369

Summary: We provide a class of QFTs which exhibit dissipation above a threshold energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling the fields to additional degrees of freedom (heavy fields) which introduce the rest frame. Using the equivalence principle, we define these theories in arbitrary curved spacetime. We then confront the trans-Planckian question of inflationary cosmology. When dissipation increases with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. However it still exists as a composite operator made with the additional fields. And when these are in their ground state, the standard power spectrum obtains if the threshold energy is much larger that the Hubble parameter. In fact, as the energy redshifts below the threshold, the composite operator behaves as if it were a free field endowed with standard vacuum fluctuations. The relationship between our models and the braneworld scenarios studied by Libanov and Rubakov displaying similar effects is discussed. The signatures of dissipation will be studied in a forthcoming paper.

MSC:

83F05 Relativistic cosmology
81T20 Quantum field theory on curved space or space-time backgrounds
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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