  We study Lorentzian wormholes in the ghost-free bigravity theory described by
two metrics, g and f. Wormholes can exist if only the null energy condition is
violated, which happens naturally in the bigravity theory since the graviton
energy-momentum tensors do not apriori fulfill any energy conditions. As a
result, the field equations admit solutions describing wormholes whose throat
size is typically of the order of the inverse graviton mass. Hence, they are as
large as the universe, so that in principle we might all live in a giant
wormhole. The wormholes can be of two different types that we call W1 and W2.
The W1 wormholes interpolate between the AdS spaces and have Killing horizons
shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes
imaginary in the AdS zone, hence the gravitons behave as tachyons, but since
the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon
instability. For the W2 wormholes the g-geometry is globally regular and in the
far field zone it becomes the AdS up to subleading terms, its throat can be
traversed by timelike geodesics, while the f-geometry has a completely
different structure and is not geodesically complete. There is no evidence of
tachyons for these solutions, although a detailed stability analysis remains an
open issue. It is possible that the solutions may admit a holographic
interpretation.
