The need to renormalize the cosmological constant

We consider the massless, minimally coupled scalar on de Sitter background. Although the 1 -loop divergences of the graviton 1PI 2 -point function are canceled by the usual Weyl (C-2) and Eddington (R-2) counterterms, there is still a finite, nonzero contribution to the graviton 1 -point function. Unless this is canceled by a finite renormalization of the cosmological constant, the 1PI 2 -point function will not be conserved, nor will the parameter "H" correspond to the actual Hubble constant. We argue that a similar finite renormalization of the cosmological constant is necessary in pure gravity, and that this must be done when solving the effective field equations for 1 -loop corrections to the graviton wave function and to the force of gravity.