Meta Note: This post is my 2,700th post on this blog (over a little less than thirteen and a half years). It is my 12,080th post on this blog and my Wash Park Prophet blog combined (over a little less than nineteen and a half years).
Gravitons gravitate in proportion to their mass-energy which is a function of their gravitational wave frequency in the case of a massless graviton, even if they have no rest mass. But this effect is usually ignored.
Exploring massive graviton theories, involving low mass, relativistic gravitons can reveal some of these effects which shouldn't actually depend on gravitons having rest mass.
The biggest problem with massive graviton theories is that they qualitatively and not quantitatively change how gravity works, by giving rise to different numbers of degrees of freedom than are found in general relativity.
Relations between the graviton mass and the cosmological constant Λ have led to some interesting implications. We show that in any approach which leads to a direct correlation between the graviton mass and Λ, 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.
Oem Trivedi, Abraham Loeb, "On the Cosmological Constant-Graviton Mass correspondence" arXiv:2411.12757 (November 15, 2024).
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