Quantum metrics with very low action in $R+R^2$ 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 = hL P lanck , with h = 0, 1, ..., N and N up to 10 5 . The Lagrangian is of the form √ g(R + αR 2 ) (in units c = = G = 1) and the action is positivedefinite, allowing the use of a standard Metropolis algorithm with update probability exp(−β∆S). By minimizing the R + R 2 action with respect to conformal modes, Bonanno and Reuter have recently found analytical evidence of a non-trivial "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 g rr is significantly different from flat space. The scaling properties of S and g rr are investigated in dependence on N and β.