||On the possible geometrical origin of the cosmological constant in the gauge theory of gravity
The purpose of this paper is to search for the possible geometrical origin of the cosmological constant based on the MacDowell-Mansouri gravity, which was first proposed in 1977 as a method of treating gravity just like other interactions in the sense of gauge theory, namely, starting from a quadratic Lagrangian. In order to realize this project, we introduce mathematical instruments, namely the vector bundle theory in first and, after trying to apply this instrument to describe the Einstein's general theory of relativity, the principal bundle theory, in second. Also the latter theory will be applied to describe the Yang-Mills gauge theory. Finally, in the last few sections, we introduce the Klein-Cartan gauge theory and its reductive case including the Inönü-Wigner contraction, and the MacDowell-Mansouri gravity of the FLRW-spacetime in vacuum as an application of the Klein-Cartan gauge theory. In these last few sections we show that the cosmological term is a priori contained in the theory, and when we perform the Inönü-Wigner contraction the cosmological term drops out, and then we came back to the Einstein's original theory. The physical idea is given by the title of this paper. My thesis is devoted to a mathematical realization of this idea, based on the existing literature about the gauge theory of gravity.
首都大学東京, 2017-03-25, 修士（理学）