  Causal Dynamical Triangulations (CDT) is a proposal for a theory of quantum
gravity, which implements a path-integral quantization of gravity as the
continuum limit of a sum over piecewise flat spacetime geometries. We use Monte
Carlo simulations to analyse the phase transition lines bordering the
physically interesting de Sitter phase of the four-dimensional CDT model. Using
a range of numerical criteria, we present strong evidence that the so-called
A-C transition is first order, while the B-C transition is second order. The
presence of a second-order transition may be related to an ultraviolet fixed
point of quantum gravity and thus provide the key to probing physics at and
possibly beyond the Planck scale.
