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Causal Dynamical Triangulations is a background independent approach toquantum gravity. In this paper we introduce a phenomenological transfer matrixmodel, where at each time step a reduced set of quantum states is used. Thestates are solely characterized by the discretized spatial volume. Using MonteCarlo simulations we determine the effective transfer matrix elements andextract the effective action for the scale factor. In this framework no degreesof freedom are frozen, however, the obtained action agrees with theminisuperspace model.

The transfer matrix in four-dimensional Causal Dynamical Triangulations