ICTS

We explicitly construct the most general four graviton S matrix  generated by a  local $k$ derivative Lagrangian describing the self interactions of gravitons. In $D \leq 6$ we demonstrate that the Einstein S matix is the only one of this infinite set that grows no faster than $s^2$ in the Regge (i.e. fixed $t$) limit. In $D\geq 7$ we demonstrate that there is one additional S matrix with this property, and we construct the same.  We then conjecture that the property  that S matrices grow no faster than  $s^2$ af fixed $t$ is true of all physically acceptable classical theories. Our conjecture, if correct, implies that Einstein gravity is the only `consistent' local (i.e. finite number of higher derivatives) theory of gravity in $D \leq 6$.