Triangulation Model Of Quantum Gravity Research Articles

The transfer matrix in four-dimensional CDT

Abstract The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.

Continuum random combs and scale-dependent spectral dimension

Numerical computations have suggested that in causal dynamical triangulation models of quantum gravity (CDT) the effective dimension of spacetime in the ultraviolet (UV) is lower than in the infrared (IR). In this paper we develop a simple model based on the previous work on random combs, which share some of the properties of CDT, in which this effect can be shown to occur analytically. We construct a definition for short- and long-distance spectral dimensions and show that the random comb models exhibit scale-dependent spectral dimension defined in this way. We also observe that a hierarchy of apparent spectral dimensions may be obtained in the cross-over region between UV and IR regimes for suitable choices of the continuum variables. Our main result is valid for a wide class of tooth length distributions thereby extending previous work on random combs by Durhuus et al.

Singular structure in 4D simplicial gravity

We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the gravitational coupling is varied appears to be first order.