Reheating-volume measure in the string theory landscape

I recently proposed the “reheating-volume” (RV) prescription as a possible solution to the measure problem in “multiverse” cosmology. The goal of this work is to extend the RV measure to scenarios involving bubble nucleation, such as the string theory landscape. In the spirit of the RV prescription, I propose to calculate the distribution of observable quantities in a landscape that is conditioned in probability to nucleate a finite total number of bubbles to the future of an initial bubble. A general formula for the relative number of bubbles of different types can be derived. I show that the RV measure is well defined and independent of the choice of the initial bubble type, as long as that type supports further bubble nucleation. Applying the RV measure to a generic landscape, I find that the abundance of Boltzmann brains is always negligibly small compared with the abundance of ordinary observers in the bubbles of the same type. As an illustration, I present explicit results for a toy landscape containing four vacuum states, and for landscapes with a single high-energy vacuum and a large number of low-energy vacua.

Figure 1

An example simulation of “eternal inflation in a box” in two spatial dimensions. Bubbles ($H$ regions) are represented in comoving coordinates by squares. Dark shades indicate bubbles of terminal types. Other shades correspond to nested bubbles of various nonterminal (recyclable) types. For the purposes of visual illustration, nucleation rates were chosen of order one, and colored lines were drawn at bubble boundaries.