In this thesis, the author considers quantum gravity to investigate the mysterious origin of our universe and its mechanisms. He and his collaborators have greatly improved the analyticity of two models: causal dynamical triangulations (CDT) and n-DBI gravity, with the space-time foliation which is one common factor shared by these two separate models. In the first part, the analytic method of coupling matters to CDT in 2-dimensional toy models is proposed to uncover the underlying mechanisms of the universe and to remove ambiguities remaining in CDT. As a result, the wave function of the 2-dimensional universe where matters are coupled is derived. The behavior of the wave function reveals that the Hausdorff dimension can be changed when the matter is non-unitary. In the second part, the n-DBI gravity model is considered. The author mainly investigates two effects driven by the space-time foliation: the appearance of a new conserved charge in black holes and an extra scalar mode of the graviton. The former implies a breakdown of the black-hole uniqueness theorem while the latter does not show any pathological behavior.

Provides a pedagogical review of two quantum gravity models: causal dynamical triangulations, with the aid of numerous illustrations, and n-DBI gravity Contains many examples of and supplements to the analytic method for computing the wave function of the Universe in 2-dimensional CDT Nominated as an outstanding Ph.D. thesis by Nagoya University's Physics Department in 2013 Includes supplementary material: sn.pub/extras

Autorentext
Dr.Yuki Sato
Nagoya University
Department of Physics
Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

Inhalt
Introduction.- Causal Dynamical Triangulation.- n-DBI Gravity.- Summary.- Appendices.