Stabilized Quantum Gravity: Stochastic Interpretation and Numerical Simulation

TL;DR

This paper demonstrates that stabilized quantum gravity can be understood through stochastic quantization, providing a new approach with numerical simulations that reveal insights into the cosmological constant problem.

Contribution

It establishes the equivalence of stabilized quantum gravity to Langevin evolution and reports initial numerical results on lattice models.

Findings

System remains in broken phase with non-zero determinant of tetrad

Negative free energy observed near zero cosmological constant

Numerical simulations suggest relevance to the cosmological constant problem

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.