Light ray fluctuations in simplicial quantum gravity

Abstract

A non-perturbative study on the quantum fluctuations of light ray propagation through a quantum region of spacetime is long overdue. Within the theory of Lorentzian simplicial quantum gravity, we compute the probabilities for a test light ray to land at different locations after travelling through a symmetry-reduced box region in 2, 3 and 4 spacetime dimensions. It is found that for fixed boundary conditions, light ray fluctuations are generically large when all coupling constants are relatively small in absolute value. For fixed coupling constants, as the boundary size is decreased light ray fluctuations first increase and then decrease in a 2D theory with the cosmological constant, Einstein–Hilbert and R-squared terms. While in 3D and 4D theories with the cosmological constant and Einstein–Hilbert terms, as the boundary size is decreased light ray fluctuations just increase. Incidentally, when studying 2D quantum gravity we show that the global time-space duality with the cosmological constant and Einstein–Hilbert terms noted previously also holds when arbitrary even powers of the Ricci scalar are added. We close by discussing how light ray fluctuations can be used in obtaining the continuum limit of non-perturbative Lorentzian quantum gravity.