Confronting the trans-Planckian question of inflationary cosmology with dissipative effects

TL;DR

This paper introduces dissipative quantum field theories that break Lorentz invariance at high energies, examining their impact on inflationary perturbations and the resulting power spectrum in cosmology.

Contribution

It proposes a class of Lorentz-violating QFTs with dissipation above a threshold, preserving unitarity via coupling to heavy fields, and analyzes their effects on inflationary perturbations.

Findings

Dissipation causes adiabatic perturbations to be damped at inflation start.

Standard power spectrum is recovered when threshold energy exceeds Hubble parameter.

Composite operators behave as free fields below the threshold energy.

Abstract

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 Brane World scenarios studied by Libanov and Rubakov displaying similar effects is discussed. The signatures of dissipation will be studied in a forthcoming paper.