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.
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