Contribution from cosmological scalar perturbations to the angular velocity spectrum of extragalactic sources
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, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Contribution from Cosmological Scalar Perturbations to the Angular Velocity Spectrum of Extragalactic Sources A. O. Marakulina,*, O. S. Sazhinaa,b, and M. V. Sazhina,b a
Moscow State University, Moscow, 119992 Russia Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, 119992 Russia *email: [email protected]
b
Received October 1, 2011
Abstract—The possibility of the influence of adiabatic scalar perturbations on the angular velocity spectrum of extragalactic sources is considered. The multipole expansion coefficients of the angular velocity field in terms of vector spherical harmonics are calculated. We show that there is no contribution from adiabatic per turbations to the angular spectrum for a spatially flat Universe at the dusty stage, while there is a contribution only to the electric multiple coefficients at the stage of Λterm domination. The cases of longwavelength and shortwavelength perturbations are considered separately. The relationship between the multipole angular velocity spectrum and the primordial scalar perturbation spectrum is discussed. DOI: 10.1134/S106377611206009X
1. INTRODUCTION When the International Celestial Reference Frame (ICRF) [1, 2] based on longterm Very Long Baseline Interferometry (VLBI) observations of extragalactic sources was constructed, the kinematic principle of constructing reference frames was used [3]. The qua sars and other objects defining the ICRF were assumed to be located at such large distances from the observer that their possible displacements over the celestial sphere are much smaller than the presentday accuracy of observations. Therefore, the proper motions and parallaxes of these objects may be consid ered negligible. However, observations showed the extragalactic sources to have high angular velocities [4], so that the apparent linear velocities of such sources often turn out to be greater than the speed of light. There are several reasons to explain such apparent motions. One of them is the kinematic Blandford–Rees effect stemming from the fact that astronomers observe the projection of the jet from a quasar or an active galac tic nucleus; this projection moves with an apparent velocity exceeding considerably the speed of light [5, 6]. The next reason is that the path of the light ray from an extragalactic source is not a straight line but a curve, because the spacetime is nonstationary. This phenom enon arises from a variable gravitational field that can be either a scalar gravitational field with sources or a field without sources—gravitational waves. The effect of gravitational waves on the apparent positions of extragalactic radio sources was investi gated in several papers [7–10]. This method of detect ing cosmological gravitational waves turned out to be very promising and was used by several authors to
determine the upper limits for the energy density of cosmological gravitational waves. Since the apparent motions of extragalactic sources (even those widely separa
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