Stabilized Quantum Gravity: Stochastic Interpretation and Numerical Simulation

Abstract

Following the reasoning of Claudson and Halpern, it is shown that "fifth-time" stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbitrary, initial and final states. The simple restriction to a fixed final state at $t_5 \rightarrow \infty$ is sufficient to stabilize the theory. This equivalence fixes the integration measure, and suggests a particular operator-ordering, for the fifth-time action of quantum gravity. Results of a numerical simulation of stabilized, latticized Einstein-Cartan theory on some small lattices are reported. In the range of cosmological constant $\l$ investigated, it is found that: 1) the system is always in the broken phase $<det(e)> \ne 0$; and 2) the negative free energy is large, possibly singular, in the vincinity of $\l = 0$. The second finding may be relevant to the cosmological constant problem.