Eternal Inflation And Time Arrow

The cosmological model of eternal inflation predicted the presence of the multiverse.There is an interesting problem on how to introduce the time arrow for the multiverse.Based on the model introduced by Bousso and Polchinski in 2000 which predicted the discrete spectrum of the cosmological constant(BP model),and the assumptions of the simultaneous presence of the anti-de-Sitter universe,the Minkowski universe and the de-Sitter universe,we found a kind of time arrow by numerical simulation of the vacuum dynamical master equation.This kind of time arrow comes from detailed balance breaking.It is different from the usual dynamical time arrow.This time arrow appears even in the steady states with nonzero entropy production.Based on the fluctuation theorem,we quantitatively describe the irreversibility of the time arrow.We also obtained the potential and flux landscapes by numerically simulating the vacuum dynamical master equation.From the potential-flux representation,the evolution of the multiverse is determined by the potential and flux landscapes.The flux landscape provides a driving force to form the stable cycle flow in the multiverse state space.We showed the steady-state probability flux could be decomposed into some cycles,which provides a new perspective for the evolution of the multiverse.Different kinds of universes may be connected by the flux and this kind of connections do not break causal relations.