Simplicial Gravity Coupled to Scalar Matter

A model for quantized gravity coupled to matter in the form of a single scalar field is investigated in four dimensions. For the metric degrees of freedom we employ Regge's simplicial discretization, with the scalar fields defined at the vertices of the four-simplices. We examine how the continuous phase transition found earlier, separating the smooth from the rough phase of quantized gravity, is influenced by the presence of scalar matter. A determination of the critical exponents seems to indicate that the effects of matter are rather small, unless the number of scalar flavors is large. Close to the critical point where the average curvature approaches zero, the coupling of matter to gravity is found to be weak. The nature of the phase diagram and the values for the critical exponents suggest that gravitational interactions increase with distance. \vspace{24pt} \vfill