  The principle of horizon complementarity is an attempt to extend ideas about
black hole complementarity to all horizons, including cosmological ones. The
idea is that the degrees of freedom necessary to describe the interior of the
cosmic horizon of one observer in a given universe are in fact sufficient to
account for the physics of that entire universe: the remainder is just a set of
redundant copies of the interior of a single cosmic horizon. These copies must
be factored out, just as one has to factor out gauge redundancies to identify
the true degrees of freedom in gauge theory. Motivated by the observation that
quantum cosmology favours compactified negatively curved spatial sections, we
propose to use such geometries to implement horizon complementarity for eternal
Inflation. We point out that the "effective finiteness" of such universes has
important consequences for physics inside the observer's horizon: there is a
non-local effect, represented by a Casimir energy. We use our proposed
interpretation of complementarity to constrain the gravitational Casimir
coupling in two very different ways; the result is an explicit prediction for
the value of the coupling.
