  We consider quantum Einstein gravity in three dimensional de Sitter space.
The Euclidean path integral is formulated as a sum over geometries, including
both perturbative loop corrections and non-perturbative instanton corrections
coming from geometries with non-trivial topology. These non-trivial geometries
have a natural physical interpretation. Conventional wisdom states that the
sphere is the unique Euclidean continuation of de Sitter space. However, when
considering physics only in the causal patch of a single observer other
Euclidean geometries, in this case lens spaces, contribute to physical
observables. This induces quantum gravitational effects which lead to
deviations from the standard thermal behaviour obtained by analytic
continuation from the three sphere. The sum over these geometries can be
formulated as a sum over cosets of the modular group; this is the de Sitter
analog of the celebrated "black hole Farey tail." We compute the vacuum
partition function including the sum over these geometries. Perturbative
quantum corrections are computed to all orders in perturbation theory using the
relationship between Einstein gravity and Chern-Simons theory, which is checked
explicitly at tree and one-loop level using heat kernel techniques. The vacuum
partition function, including all instanton and perturbative corrections, is
shown to diverge in a way which can not be regulated using standard field
theory techniques.
