  Recent results of Hartle-Hawking wave functions on asymptotic dS boundaries
show non-normalizability, while the bulk origin is not clear. This paper
attempts to addresse this problem by studying (Kerr-)dS_3 cosmology in Einstein
gravity deformed by a minimally coupled scalar field. Various saddle-point
contributions exp[i(saddle-point action)] to the Hartle-Hawking wave functions
are computed with mini-superspace formalism. The saddle-point actions are first
obtained in the spacetime bulks by direct computation, then on the asymptotic
dS boundary by holographic renormalization. It is found that the imaginary part
of the saddle-point actions, as functions of scalar field deformation, are
generally bounded in the bulk, but can diverge to -infty on the boundary. This
can probably be a source of the scalar field-related non-normalizability of the
boundary Hartle-Hawking wave functions. For Kerr-dS_3 cosmology, some
saddle-point actions have imaginary parts diverging to -infty both in the bulk
and on the boundary, when the boundary T^2 is stretched to infinitely long.
This can be an origin of non-normalizability of the boundary Hartle-Hawking
wave functions related to temperature divergence. Finally the holographic
renormalization is extended to scalar-deformed dS_{d+1} (d>= 3) cosmologies for
the imaginary part of the saddle-point actions. The result is tested on a 5d
example, and saddle points leading to divergent contribution to the boundary
Hartle-Hawking wave function are shown to exist.
