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The quantum treatment of the 5D-warped Friedmann-Robertson-Walker universe in Schrödinger picture. (English) Zbl 1266.83178

Summary: The present paper is devoted to the time-evolving Schrödinger version of the Wheeler-De Witt equation, written for the five dimensional warped \(k=0\)-FRW Universe. For small values of the cosmological scale factor, \(a\), the wave function of the Universe is expressed in terms of the Heun Double Confluent functions, which have been intensively worked out in the last years. As expected, for large \(a\)’s, one gets the well-known Hermite associated functions. Within the semiclassical approximation, valid for large \(n\), the asymptotic representation of the Whittaker functions leads to the “free particle” behavior.

MSC:

83F05 Relativistic cosmology
83E15 Kaluza-Klein and other higher-dimensional theories
83C47 Methods of quantum field theory in general relativity and gravitational theory
83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81S10 Geometry and quantization, symplectic methods
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