Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1994-07-28
Grav.Cosmol.8:213-221,2002
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revised in 2002, LaTeX, 12 pages, G&C style, published version
Scientific paper
We consider the quantization of a general spatially homogeneous space-time belonging to an arbitrary but fixed Class A Bianchi type. Exploiting the information furnished by the quantum version of the momentum constraints, we use as variables the two simplest contractions of $C^{\alpha}_{\beta \gamma}$ and $\gamma_{\alpha \beta}$ as well as the determinant of $\gamma_{\alpha \beta}$ ; We thus arrive at an equation for the wave function in terms of these quantities. This fact enables us to treat in a uniform manner all Class A cosmologies. For these spacetimes the Langrangian used correctly reproduces Einstein's equations. We also discuss the imposition of simplifying ans\"{a}tzen at the quantum level in a way that respects the scalings of the quadratic Hamiltonian constraint.
Christodoulakis Th.
Korfiatis E.
Vagenas Elias C.
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