The Quantum Treatment of the 5D-Warped Friedmann–Robertson–Walker Universe in Schrödinger Picture

Abstract

The present paper is devoted to the time-evolving Schrodinger 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.