Classical and quantum wormholes with perfect fluids and scalar fields

Euclidean wormholes are obtained by the analytic continuation of closed recollapsing Friedmann-Robertson-Walker universes. We demonstrate this for a perfect fluid satisfying the strong energy condition. The quantum versions of such wormholes are consistent with the Hawking-Page (HP) conjecture for quantum wormholes as solutions of the Wheeler-DeWitt equation. We contrast this with a classical change of signature approach which, although might be consistent with the existence of classical wormholes for a given definition of the energy-momentum tensor of the fluid, upon quantization gives everywhere oscillatory wave functions which do not satisfy the HP conjecture.