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.
