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Simultaneous Hamiltonian Treatment of Class A Spacetimes and Reduction of Degrees of Freedom at the Quantum Level

T. Christodoulakis·E. Korfiatis·E. C. Vagenas
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Abstract

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 $C^α_{βγ}$ and $γ_{αβ}$ as well as the determinant of $γ_{αβ}$ ; 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 ansätzen at the quantum level in a way that respects the scalings of the quadratic Hamiltonian constraint.

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T. Christodoulakis, E. Korfiatis, E. C. Vagenas. 2002-10-10. Simultaneous Hamiltonian Treatment of Class A Spacetimes and Reduction of Degrees of Freedom at the Quantum Level. https://arxiv.org/abs/gr-qc/9407042

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