On Bogoliubov Transformation of Scalar Wave Functions in De Sitter Space

Abstract

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in 4 dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exist manifest horizon. We consider two type of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables.

arXiv comment16 pages, OU-HET 202, LMU-TPW 94-13

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• New Spherical Scalar Modes on the de Sitter Expanding Universe
• Symmetry Breaking in the Static Coordinate System of de Sitter Spacetime
• Atlas of Coordinate Charts on de Sitter Spacetime
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• Weber-Schafheitlin integrals with arbitrary exponent
• Discrete symmetries determining scalar quantum modes on the de Sitter spacetime