A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations

Abstract

We study a lattice regularization of the gravitational path integral--causal dynamical triangulations--for (2+1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of fixed intrinsic geometries. For spatial topology of a 2-sphere, we determine the form of the Einstein-Hilbert action supplemented by the Gibbons-Hawking-York boundary terms within the Regge calculus of causal triangulations. Employing this action we numerically simulate a variety of transition amplitudes from the past boundary to the future boundary. To the extent that we have so far investigated them, these transition amplitudes appear consistent with the gravitational effective action previously found to characterize the ground state of quantum spacetime geometry within the Euclidean de Sitter-like phase. Certain of these transition amplitudes convincingly demonstrate that the so-called stalks present in this phase are numerical artifacts of the lattice regularization, seemingly indicate that the quantization technique of causal dynamical triangulations differs in detail from that of the no-boundary proposal of Hartle and Hawking, and possibly represent the first numerical simulations of portions of temporally unbounded quantum spacetime geometry within the causal dynamical triangulations approach. We also uncover tantalizing evidence suggesting that Lorentzian not Euclidean de Sitter spacetime dominates the ground state on sufficiently large scales.

27 pages, 14 figures, 1 table; reflects published version

References in corpus (12)

• Nonperturbative Quantum Gravity
• The Nonperturbative Quantum de Sitter Universe
• Second- and First-Order Phase Transitions in CDT
• The Semiclassical Limit of Causal Dynamical Triangulations
• 2d CDT is 2d Horava-Lifshitz quantum gravity
• Renormalization Group Flow in CDT
• Scaling Exponents for Lattice Quantum Gravity in Four Dimensions
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
• 3D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model

Cited by in corpus (14)

• Dimension and Dimensional Reduction in Quantum Gravity
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Quantum Gravity on the computer: Impressions of a workshop
• Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
• Scale-dependent homogeneity measures for causal dynamical triangulations
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Scaling analyses of the spectral dimension in 3-dimensional causal dynamical triangulations
• Setting the physical scale of dimensional reduction in causal dynamical triangulations
• The phase structure and effective action of 3D CDT at higher spatial genus
• A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Making the case for causal dynamical triangulations
• Landau Theory of Causal Dynamical Triangulations