General Relativity from Causality
  We study large families of theories of interacting spin 2 particles from the
point of view of causality. Although it is often stated that there is a unique
Lorentz invariant effective theory of massless spin 2, namely general
relativity, other theories that utilize higher derivative interactions do in
fact exist. These theories are distinct from general relativity, as they permit
any number of species of spin 2 particles, are described by a much larger set
of parameters, and are not constrained to satisfy the equivalence principle. We
consider the leading spin 2 couplings to scalars, fermions, and vectors, and
systematically study signal propagation in all these other families of
theories. We find that most interactions directly lead to superluminal
propagation of either a spin 2 particle or a matter particle, and interactions
that are subluminal generate other interactions that are superluminal. Hence,
such theories of interacting multiple spin 2 species have superluminality, and
by extension, acausality. This is radically different to the special case of
general relativity with a single species of minimally coupled spin 2, which
leads to subluminal propagation from sources satisfying the null energy
condition. This pathology persists even if the spin 2 field is massive. We
compare these findings to the analogous case of spin 1 theories, where higher
derivative interactions can be causal. This makes the spin 2 case very special,
and suggests that multiple species of spin 2 is forbidden, leading us to
general relativity as essentially the unique internally consistent effective
theory of spin 2.
