On the Cosmological Constant-Graviton Mass correspondence

TL;DR

The paper demonstrates that in theories linking graviton mass to the cosmological constant, the resulting graviton wavelength exceeds the observable universe, rendering such models observationally irrelevant.

Contribution

It shows that any direct correlation between graviton mass and the cosmological constant implies a superhorizon graviton wavelength, challenging their observational significance.

Findings

Graviton Compton wavelength exceeds the horizon scale in these models.

Direct graviton mass-$\Lambda$ relations imply no observable effects.

Such models are of no current observational relevance.

Abstract

Relations between the graviton mass and the cosmological constant $\Lambda$ have led to some interesting implications. We show that in any approach which leads to a direct correlation between the graviton mass and $\Lambda$, 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.