  Gravitational instantons ''Lambda-instantons'' are defined here for any given
value Lambda of the cosmological constant. A multiple of the Euler
characteristic appears as an upper bound for the de Sitter action and as a
lower bound for a family of quadratic actions. The de Sitter action itself is
found to be equivalent to a simple and natural quadratic action. In this paper
we also describe explicitly the reparameterization and duality invariances of
gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant
doubling of the fields using the Hamiltonian formalism leads to first order
time evolution with manifest duality symmetry. As a special case we recover the
linear flat space result of Henneaux and Teitelboim by a smooth limiting
process.
