Quantum Cosmological Perturbations of Multiple Fluids

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).

20 pages, matches PRD published version

References in corpus (18)

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Cited by in corpus (15)

• Particle Creation in Bouncing Cosmologies
• Consistent Scalar and Tensor Perturbation Power Spectra in Single Fluid Matter Bounce with Dark Energy Era
• Viable tensor-to-scalar ratio in a symmetric matter bounce
• Primordial features from ekpyrotic bounces
• The de Broglie-Bohm Quantum Theory and its Application to Quantum Cosmology
• Viable scalar spectral tilt and tensor-to-scalar ratio in near-matter bounces
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Fermion Production in Bouncing Cosmologies
• Hamiltonian formalism and gauge-fixing conditions for cosmological perturbation theory
• Vector perturbations in bouncing cosmology
• New formalism to define vacuum states for scalar fields in curved space-times
• Primordial Black Hole Formation in a Dust Bouncing Model
• Evolution of Quantum Nonequilibrium for Coupled Harmonic Oscillators
• Viable Curvaton Models from the $f_{NL}$ Parameter
• Selected Topics in Numerical Methods for Cosmology