Vacuum Fluctuations and the Small Scale Structure of Spacetime

We show that vacuum fluctuations of the stress-energy tensor in two-dimensional dilaton gravity lead to a sharp focusing of light cones near the Planck scale, effectively breaking space up into a large number of causally disconnected regions. This phenomenon, called “asymptotic silence” when it occurs in cosmology, might help explain several puzzling features of quantum gravity, including evidence of spontaneous dimensional reduction at short distances. While our analysis focuses on a simplified two-dimensional model, we argue that the qualitative features should still be present in four dimensions.

Figure 1

Probability of the expansion diverging to $-\infty$ as a function of Planck time steps. The solid line is the exponential distribution (11).