Lorentzian quantum cosmology goes simplicial

Abstract

We employ the methods of discrete (Lorentzian) Regge calculus for analysing Lorentzian quantum cosmology models with a special focus on discrete analogues of the no-boundary proposal for the early universe. We use a simple 4-polytope, a subdivided 4-polytope and shells of discrete 3-spheres as triangulations to model a closed universe with cosmological constant, and examine the semiclassical path integral for these different choices. We find that the shells give good agreement with continuum results for small values of the scale factor and in particular for finer discretisations of the boundary 3-sphere, while the simple and subdivided 4-polytopes can only be compared with the continuum in certain regimes, and in particular are not able to capture a transition from Euclidean geometry with small scale factor to a large Lorentzian one. Finally, we consider a closed universe filled with dust particles and discretised by shells of 3-spheres. This model can approximate the continuum case quite well. Our results embed the no-boundary proposal in a discrete setting where it is possibly more naturally defined, and prepare for its discussion within the realm of spin foams.

47 pages, 19 figures; v4: fixed a few typos, added some references to figures

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• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• Quantum cosmology of pure connection general relativity
• Truly Lorentzian quantum cosmology
• Light ray fluctuations in simplicial quantum gravity
• Light ray fluctuation and lattice refinement of simplicial quantum gravity
• Discrete Gravity with Local Lorentz Invariance