Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability distribution for the quantum universe   We determine the inner product on the Hilbert space of wavefunctions of the
universe by imposing the Hermiticity of the quantum Hamiltonian in the context
of the minisuperspace model. The corresponding quantum probability density
reproduces successfully the classical probability distribution in the $\hbar
\to 0$ limit, for closed universes filled with a perfect fluid of index $w$.
When $-1/3<w\le 1$, the wavefunction is normalizable and the quantum
probability density becomes vanishingly small at the big bang/big crunch
singularities, at least at the semi-classical level. Quantum expectation values
of physical geometrical quantities, which diverge classically at the
singularities, are shown to be finite.

10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph