Bootstrapping gravity: a consistent approach to energy-momentum
  self-coupling
  It is generally believed that coupling the graviton (a classical Fierz-Pauli
massless spin-2 field) to its own energy-momentum tensor successfully recreates
the dynamics of the Einstein field equations order by order; however the
validity of this idea has recently been brought into doubt [1]. Motivated by
this, we present a graviton action for which energy-momentum self-coupling is
indeed consistent with the Einstein field equations. The Hilbert
energy-momentum tensor for this graviton is calculated explicitly and shown to
supply the correct second-order term in the field equations; in contrast, the
Fierz-Pauli action fails to supply the correct term. A formalism for
perturbative expansions of metric-based gravitational theories is then
developed, and these techniques employed to demonstrate that our graviton
action is a starting point for a straightforward energy-momentum self-coupling
procedure that, order by order, generates the Einstein-Hilbert action (up to a
classically irrelevant surface term). The perturbative formalism is extended to
include matter and a cosmological constant, and interactions between
perturbations of a free matter field and the gravitational field are studied in
a vacuum background. Finally, the effect of a non-vacuum background is
examined, and the graviton is found to develop a non-vanishing ``mass-term'' in
the action.
