The solution of a wave equation in two-dimension anti-de Sitter space

Abstract

A solution of a wave equation on a surface of a one-sheet hyperboloid is found in the article. The surface is considered as two-dimension model of the accelerated Universe. It is shown the phase velocity increases in the global reference frame, but it is constant with regard to a concomitant one. Allowable frequencies and wave numbers are discrete and decreasing with time proportionally to the space curvature. The performed calculations show the discreteness step has to be much less than present-day experimental possibilities of measurements.