Quantum metrics with very low action in R+R2 gravity

Abstract

We have run numerical simulations of Euclidean lattice quantum gravity for metrics which are time-independent and spherically symmetric. The radial variable is discretized as r=hLPlanck, with h=0,1,⋯,N and N up to 105. The Lagrangian is of the form g(R+αR2) (in units c= =G=1) and the action is positive-definite, allowing the use of a standard Metropolis algorithm with update probability exp(-βΔS). By minimizing the R+R2 action with respect to conformal modes, Bonanno and Reuter have recently found analytical evidence of a nontrivial "rippled"ground state resembling a kinetic condensate of QCD. Our simulations at low but finite temperature (T=β-1) also display strong localized oscillations of the metric, whose total action S remains thanks to the indefinite sign of R. The average metric grr is significantly different from flat space. The scaling properties of S and grr are investigated in dependence on N and β.