Five-Dimensional Cosmological Model With The Kaluza-Klein Metric And Related Research

This paper used the canonical quantization method to calculate the Wheeler -Dewitt (W-D) equation, and looked for special solutions of the W-D equation by separation of variables. Using the Kaluza-Klein(K-K) theory, the four-dimensional space-time was expanded to the five-dimensional space-time. Under the basis of the K-K metric, solving two five-dimensional cosmological model of Einstein field equation not considering gravitational constant and cosmological constant, and with the field equations of the space-time, obtained some conclusions of the universe expansion, finally discussed the five-dimensional cosmological model with the variable gravitational constant and cosmological constant, contained some natures of the variation of gravitational constant and cosmological constant with time.The full text is divided into five chapters:Chapter I introduced the traditional K-K theory and Brans-Dicke (B-D) theory of the variable-gravity theories, and then a brief description of the Space-Time-Matter theory proposed by Wesson.Chapter II introduced the W-D equation in the four-dimensional R + R2 theory of gravity, and looked for special solutions of the W-D equation by separation of variables.Chapter III respectively calculated a simple vacuum five-dimensional cosmological model and a five-dimensional cosmological model with a time-dependent equation of state in Wesson's theory by introducing the K-K metric, and then analyzed the solutions of the field equation,focusing discussed on problems of the universe expansion. Chapter IV mainly solved the five-dimensional cosmological model with the variable gravitational constant and cosmological constant using the K-K metric, and analyzed the solutions of the field equation, obtained some conclusions of the gravitational constant G and cosmological constantΛvaries with time.Chapter V Summed up.