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

CHAPTER 10Infinities in CosmologyMichael Heller10.1 IntroductionTraditionally, the problem of infinity in cosmology appeared in the form of questionsconcerning space and time. These questions were notoriously difficult and led toparadoxes. Does space extend to infinity? If so, how can something by definitionbeyond empirical control be a subject matter of scientific inquiry? If not, what isbeyond the edges of space? Similar questions were involved in the time problem: Iftime had a beginning, what was “before” the beginning? If the age of the universeis infinite, what supplies infinite amounts of energy indispensable to compensate fordissipative losses? Relativistic cosmology did not solve these questions; it only tamedthem by elaborating strict mathematical tools, in terms of which they could be expressedwhile awaiting more empirical data that would help to further elucidate them.Quite recently, the problem of infinity has emerged in speculations in cosmologyon the, so to speak, metalevel. Wanting to neutralize difficult problems related tothe initial conditions of the temporal beginning of the universe, some people started tospeculate about “all possible universes.” If all possibilities are implemented somewherein the huge collection of “everything,” then even the most intricate questions losetheir disturbing force. The strangest things just happen (an infinite number of times)someplace. If we live in this extremely strange world of ours, this is because “moreusual” worlds do not admit the existence of the “intelligent observer.” In this approach,the old problems with space and time infinities of our world have been superseded by themany-faceted infinity problem of the “multiverse” (the name recently coined for thecollection of all possible universes). However, the point is that this approach willremain a vague ideology unless we are able to at least tame it with the help of strictmathematical concepts, as was the case with space and time infinities in relativisticcosmology. 11 There are a great variety of interpretations of the term “multiverse.” See, for instance, a “list” composed byTegmark (2007); some items on his list are rather vague. There are attempts to introduce some rigor in this area;see, for instance, Ellis (2007) orMcCabe(2005).218