Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

186 cosmological intimations of infinityFigure 8.4. A conformal “slice” for false-vacuum driven past-eternal inflation as proposedby Aguirre and Gratton (2002). Bubbles are shown in a background de Sitter space, withJ − representing a (null) surface on which cosmological boundary conditions are placed byspecifying that no bubbles exist there; it is the boundary of the region covered by t > −∞,where t is the time variable in which the universe is statistically time translation invariant. The“arrow of time” points away from this surface, so that the entire universe is effectively timereversal invariant, while each bubble has a well-defined arrow of time pointing away from theinflating phase.bubble nucleation were not accounted for) is zero. This is possible because the inflatingregion is an infinite fractal of dimension (very slightly) less than three. This is not terriblymysterious; it is just like an infinite rod in 3-space, which takes up a finite volume but avanishing volume fraction because its dimensionality is less than three. 7 Although there is no initial time (−∞