Quantum metrics with very low action in $R+R^2$ gravity

G. Modanese

doi:10.1103/PhysRevD.103.106020

paper

Quantum metrics with very low action in $R + R^{2}$ gravity

arXiv:2104.03914 · doi:10.1103/PhysRevD.103.106020

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 $r = h L_{P l an c k}$ , with $h = 0, 1, ..., N$ and $N$ up to $1 0^{5}$ . The Lagrangian is of the form $g (R + α R^{2})$ (in units $c = ℏ = G = 1$ ) and the action is positive-definite, allowing the use of a standard Metropolis algorithm with update probability $exp (- β Δ S)$ . 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 $≪ ℏ$ thanks to the indefinite sign of $R$ . The average metric $⟨ g_{r r} ⟩$ is significantly different from flat space. The scaling properties of $S$ and $⟨ g_{r r} ⟩$ are investigated in dependence on $N$ and $β$ .

arXiv comment13 pages, 7 figures

Quantum metrics with very low action in $R + R^{2}$ gravity

Abstract

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Quantum metrics with very low action in R+R2 gravity

Abstract

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Cited by in corpus (2)

Quantum metrics with very low action in $R + R^{2}$ gravity