Diffeomorphism-invariant action principles for trace-free Einstein gravity

Abstract

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.