  Trace-free Einstein gravity is a theory of gravity that is an alternative to
general relativity, wherein the cosmological constant arises as an integration
constant. However, there are no fully diffeomorphism-invariant action
principles available that lead to the equations of motion of this theory.
Unimodular gravity comes close to this idea, but it relies on action principles
that are invariant only under volume-preserving diffeomorphisms. We present a
real $BF$-type action principle for trace-free Einstein gravity that is fully
diffeomorphism-invariant and does not require any unimodular condition or
nondynamical fields. We generalize this action principle by giving another one
involving a free parameter.
