Boundary terms in cosmological models and their quantization

We analyze the boundary terms emerging from a class of cosmological models which are linear either in the extrinsic or the scalar curvature, and involve up to second derivative terms in the Lagrangians describing them. In the classical theory we explicitly identify the constraints. The algebra of first-class constraints results isomorphic to the triangular lower algebra of SL(2,ℝ) whose associated Lie group is non-unimodular. We then pursue to complete the quantization for our systems by considering recent proposals to canonically quantize nonunimodular groups by enlarging the group structure, which in turn, brings modifications to the quantum potentials appearing in the Wheeler-DeWitt equations. As stated, the modifications on these potentials are related to the boundary terms appearing in our approach. A comparison with naïve Dirac quantization is also analyzed. © Electronic Journal of Theoretical Physics.

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