A stochastic measure for eternal inflation

摘要: We use the stochastic approach to investigate a measure for slow roll eternal inflation. The probability for the universe to have a given Hubble radius can be calculated in this framework. In a solvable model, it is shown that the probability for the universe to evolve from a state with a smaller Hubble radius to one with a larger Hubble radius is dominated by the classical probability without the stochastic source, while the probability for the universe to evolve from a state with a larger Hubble radius to one with a smaller one is suppressed by exp(-Delta S), where the de Sitter entropy S arises naturally in this stochasticapproach.