on piecewise flat geometries of the Einstein-Hilbert action in the path integral (\[eq:pigrav\]), which in CDT quantum gravity is done following Regge’s prescription [@regge]. One should point out that models of the type we are studying tend to be very robust with respect to changes in the precise form of the action (which obviously is subject to discretization ambiguities) and of the configuration space, in the sense that a wide range of different regularizations and kinematical ingredients will lead to the same continuum physics, if the latter can be defined meaningfully. An exception to this is of course the imposition of causality constraints, which distinguishes CDT from DT quantum gravity and leads in all dimensions studied so far to genuinely different continuum results. In two dimensions, this can be demonstrated exactly, for example, by comparing specific observables and critical exponents, since the CDT model can be solved analytically [@al]. In higher dimensions, information about the behaviour of observables comes primarily from numerical simulations: three-dimensional CDT quantum gravity has only been solved partially and for restricted classes of triangulations [@blz], while in four dimensions analytical methods are mostly unavailable and one must resort to Monte Carlo simulations to extract physical results.

