Answering a basic objection to bang/crunch holography

Abstract

The current cosmic acceleration does not imply that our Universe is basically de Sitter-like: in the first part of this work we argue that, by introducing matter into anti-de Sitter spacetime in a natural way, one may be able to account for the acceleration just as well. However, this leads to a Big Crunch, and the euclidean versions of Bang/Crunch cosmologies have [apparently] disconnected conformal boundaries. As Maldacena and Maoz have recently stressed, this seems to contradict the holographic principle. In the second part we argue that this "double boundary problem" is a matter not of geometry but rather of how one chooses a conformal compactification: if one chooses to compactify in an unorthodox way, then the appearance of disconnectedness can be regarded as a coordinate effect. With the kind of matter we have introduced here, namely a euclidean axion, the underlying compact euclidean manifold has an unexpectedly non-trivial topology: it is in fact one of the 75 possible underlying manifolds of flat compact four-dimensional euclidean spaces. © SISSA/ISAS 2004.