Predictability crisis in inflationary cosmology and its resolution

Models of inflationary cosmology can lead to variation of observable parameters (''constants of nature'') on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated in the literature. Because of the infinite thermalized volume resulting from eternal inflation, it has proved difficult to obtain a meaningful and unambiguous probability distribution for observables, in particular due to the gauge dependence. In the present paper, we further develop the gauge-invariant procedure proposed in a previous work for models with a continuous variation of constants. The recipe uses an unbiased selection of a connected piece of the thermalized volume as sample for the probability distribution. To implement the procedure numerically, we develop two methods applicable to a reasonably wide class of models: one based on the Fokker-Planck equation of stochastic inflation and the other based on direct simulation of inflationary spacetime. We present and compare results obtained using these methods.