Particle creation in radiation and de Sitter cosmologies: a unified treatment via the Ermakov–Lewis invariant

Abstract

In this work, we propose a unified treatment for the creation of scalar particles in de Sitter and radiation-dominated backgrounds using the Ermakov–Lewis invariant. We rely on two representations of the quantum field; the first one diagonalizes the Hamiltonian, while the second diagonalizes the invariant. The Bogoliubov transformation between these two representations enables us to extract an analytical expression of the time-dependent particle number. For a radiation-dominated universe, the particle number dynamics is shown to go through three phases: An adiabatic phase where the particle number is practically zero, a non-adiabatic phase characterized by quick growth and oscillatory behavior, and finally an adiabatic phase where the particle number relaxes to a constant limit. In de Sitter space, however, and especially when the mass of the field is comparable to the Hubble constant, the particle number continues to oscillate without reaching any constant limit. In the case when the universe undergoes a transition from a de Sitter phase to a radiation-dominated era, the particle number approaches a constant value at late times. This asymptotic particle number shows interference effects in the infrared region induced by successive Bogoliubov transformations associated with the cosmological transition.