Quantum Cosmological Perturbations of Multiple Fluids

TL;DR

This paper develops a formalism for quantizing and evolving cosmological perturbations in multiple fluids, ensuring a consistent vacuum definition and unitary evolution, applicable to complex models beyond single-field scenarios.

Contribution

It introduces a general Hamiltonian formalism for multiple fluids without background equations of motion, enabling consistent quantization and initial condition setting.

Findings

Particle creation is well-defined with an appropriate vacuum choice.

The formalism is valid for adiabatically varying couplings, not just small interactions.

Common variables may lead to ill-defined vacua, highlighting the importance of variable choice.

Abstract

The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).