Confronting the trans-Planckian question of inflationary cosmology with dissipative effects
Résumé
We provide a class of QFTs which exhibit dissipative effects 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 which has been so far studied with dispersive models. When dissipative effects increase with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. Hence it is given by a composite operator made with the additional fields. Nevertheless, when these are in their ground state, and when the threshold energy is much larger that the Hubble parameter, the standard power spectrum obtains. Indeed, as the energy redshifts below the threshold, much before horizon exit, the composite operator behaves as if it were a free field endowed with standard vacuum fluctuations. The relationship between our models and Brane World scenarios studied by Libanov and Rubakov is discussed.