1305.2932 (Joshua H. Cooperman et al.)

A first look at transition amplitudes in (2+1)-dimensional causal
dynamical triangulations    [PDF]

Joshua H. Cooperman, Jonah Miller

We study a lattice regularization of the gravitational path integral--causal dynamical triangulations--for (2+1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of fixed intrinsic geometries. For spatial topology of a 2-sphere, we determine the form of the Einstein-Hilbert action supplemented by the Gibbons-Hawking-York boundary terms within the Regge calculus of causal triangulations. Employing this action we numerically simulate a variety of transition amplitudes from the past boundary to the future boundary. To the extent that we have so far investigated them, these transition amplitudes appear consistent with the gravitational effective action previously found to characterize the ground state of quantum spacetime geometry within the de Sitter-like phase. Certain of these transition amplitudes convincingly demonstrate that the so-called stalks present in this phase are numerical artifacts of the lattice regularization, seemingly indicate that the quantization technique of causal dynamical triangulations differs from that of the no-boundary proposal of Hartle and Hawking, and possibly represent the first numerical simulations of portions of temporally unbounded quantum spacetime geometry within the causal dynamical triangulations approach.

View original: http://arxiv.org/abs/1305.2932