N ov 2 00 7 A 2 D model of Causal Set Quantum Gravity

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this “entropy problem” in a model of causal set quantum gravity corresponding to a discretisation of 2D spacetimes. Using results from the theory of partial orders we show that, in the large volume or continuum limit, its partition function is dominated by causal sets which approximate to a region of 2D Minkowski space. This model of causal set quantum gravity thus overcomes the entropy problem and predicts the emergence of a physically reasonable geometry. In approaches to quantum gravity where the continuum is replaced by a more primitive entity, manifoldlikeness is typically a feature of only a small proportion of the configurations. In order to obtain the correct continuum limit, this small set of configurations needs to be dynamically favoured over the often overwhelming entropic contribution from non-manifoldlike configurations. It has been argued that some form of this “entropy problem” is of critical importance in dynamical triangulations, graph-based approaches and in causal set quantum gravity(CSQG) [1].