Discreteness of time in the evolution of the universe

Abstract

In this paper, we will first derive the Wheeler-DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler-DeWitt equation for the generalized geometry. We analyze such a deformed Wheeler-DeWitt equation in the minisuperspace approximation and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time re-parametrization invariance.Comment: 20 pages, 0 figures, To appear in IJMP