Inflation, large branes, and the shape of space

In this paper we consider the classical Euclidean wormhole solution of the Born—Infeld scalar field. The corresponding classical Euclidean wormhole solution can be obtained analytically for both very small and large \(\dot \varphi\). At the extreme limit of small \(\dot \varphi\) the wormhole solution has the same format as one obtained by Giddings and Strominger (Nuclear Physics B306, 890, 1988). At the extreme limit of large \(\dot \varphi\) the wormhole solution is a new one. The wormhole wave functions can also be obtained for both very small and large \(\dot \varphi\). These wormhole wave functions are regarded as solutions of quantum-mechanical Wheeler—Dewitt equation with certain boundary conditions.

Classical Euclidean Wormhole Solution and Wave Function for a Nonlinear Scalar Field

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.

Answering a Basic Objection to Bang/Crunch Holography

We study the classical and quantum euclidean wormholes for an empty (4+1) dimensional Kaluza–Klein universe with a positive cosmological constant and a spatially flat Robertson–Walker type metric. It is shown that classical wormholes do not exist neither for the space–time sector nor the extra dimensional sector of this model, but two spectra of quantum wormholes as the solutions of the Wheeler–DeWitt equation exist that are consistent with the Hawking–Page conjecture about the necessary boundary conditions. In the spectrum where the external scale factor R shapes the quantum wormholes the internal scale factor a may play the role of effective matter source, and in the spectrum where the internal scale factor a shapes the quantum wormholes the external scale factor R may play the role of effective matter source.

Classical and quantum wormholes in a 5D compact Kaluza–Klein theory

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.

D. H. Coule

Papers

Comment: No wormholes with real minimally coupled scalar fields