Matter contributions to the expansion rate of the universe

We consider the effect of various particles on the cosmic expansion rate relative to that of the graviton. Effectively massless fermions, gauge bosons and conformally coupled scalars make only minuscule contributions due to local conformal invariance. Minimally coupled scalars can give much stronger contributions, but they are still sub-dominant to those of gravitons on account of global conformal invariance. Unless effectively massless scalar particles with very particular couplings exist, the leading effect on the expansion rate is furnished solely by the graviton. An upper bound on the mass of such scalar particles is obtained.