Quantum Cosmological Perturbations of Multiple Fluids
  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).
