On the Cosmological Constant-Graviton Mass correspondence

Relations between the graviton mass and the cosmological constant $\mathrm{\Lambda }$ have led to some interesting implications. We show that in any approach which leads to a direct correlation between the graviton mass and $\mathrm{\Lambda }$, either through direct substitution of gravitational coupling in dispersion relations or through the linearization of Einstein equations with massive spin-2 fields, the Compton wavelength of the graviton lies in the superhorizon scale. As a result any gravitational approaches where the graviton mass is related directly to the cosmological constant are of no observational significance.