Production of phonons in an isotropic universe

TLDR: A quantum theory of irrotational perturbations of an ideal fluid in a spatially flat isotropic homogeneous cosmological model is constructed by Lifshitz and Pitaevskii as discussed by the authors.

Abstract: A quantum theory of irrotational perturbations of an ideal fluid in a spatially flat isotropic homogeneous cosmological model is constructed Two gauge-invariant canonically conjugate scalars are obtained that describe the evolution of the two physical degrees of freedom of irrotational perturbations of the matter in an expanding universe; they are analogs of the velocity potential and the density perturbation in a stationary nongravitating medium (EM Lifshitz and L P Pitaevskii, Statistical Physics, Part 2, 1978, section24) A Lagrangian and an equation of motion of second order are obtained Canonical quantization is performed, and the concept of phonons (sound quanta in a nonstationary universe) is introduced Conformal noninvariance of sound waves in an isotropic universe is proved It is shown that the mechanism of spontaneous production of phonons in the process of the cosmological expansion is the cause of the formation of the initial spectrum of adiabatic perturbations of the matter density in an isotropic Friedmann universe In the subsequent evolution in the stage after hydrogen recombination in an expanding universe the long-wavelength density fluctuations may lead to the formation of galaxies and clusters of galaxies Estimates are made of the spectrum of the primordial density fluctuations It it shown thatmore » they are in agreement with the requirements imposed on the initial spectrum by the adiabatic theory of the origin of galaxies« less