부산대학교 도서관

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 (E.M. 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 that they are in agreement with the requirements imposed on the initial spectrum by the adiabatic theory of the origin of galaxies.