Semiclassical and Continuum Limits of Four-Dimensional CDT

This chapter discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein’s gravity, based on a lattice regularization of the quantum-gravitational path integral. It is shown that inside the, so-called, de Sitter phase, one recovers a four-dimensional semiclassical universe, where behavior of the scale factor is consistent with classical solutions of Einstein’s field equations and fluctuations of the scale factor are very accurately described by a simple minisuperspace effective action. It is argued that some of the phase transitions surrounding the semiclassical phase are higher-order transitions, which opens a possibility of defining a continuum limit of CDT. Finally, it is discussed how to define the renormalization group flow in CDT and then how to search for a UV fixed point in which, in the spirit of asymptotic safety, quantum theory of gravity could become non-perturbatively renormalizable and thus valid up to arbitrarily short distance scales.