Leopold Infeld Colloquium

The Causal Dynamical Triangulation model of quantum gravity (CDT) is a proposition to regularize the path integral over space-time geometries using a lattice regularization with a discrete proper time and geometries realized as simplicial manifolds. The model admits a Wick rotation to imaginary time for each space-time configuration. Using computer simulations we determined the phase structure of the model and discovered that it predicts a de Sitter phase with a four-dimensional spherical semi-classicalbackground geometry. The model has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) imaginary times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effectiveminisuperspace action at all scales.