Answering a Basic Objection to Bang/Crunch Holography

TL;DR

This paper explores how matter in anti-de Sitter spacetime can mimic cosmic acceleration, addresses the Big Crunch and disconnected boundaries in holography, and shows that unconventional compactifications resolve apparent contradictions.

Contribution

It demonstrates that the double boundary problem in Bang/Crunch cosmologies can be resolved through alternative conformal compactifications involving Euclidean axions.

Findings

Matter in AdS can account for acceleration without de Sitter space.

Disconnection of boundaries is a coordinate effect under certain compactifications.

Underlying Euclidean manifolds have complex topologies, including 75 possible flat compact spaces.

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.