THE NATURE OF Λ AND THE MASS OF THE GRAVITON: A CRITICAL VIEW

Abstract

The observational evidence of a cosmological constant Λ raises natural questions. Is Λ a universal constant fixing the geometry of an empty universe, as fundamental as the Planck constant or the speed of light in the vacuum? Its natural place is then on the left-hand side of the Einstein equation. Is it instead something emerging from a perturbation calculation performed on the metric gμν solution of the Einstein equation and to which it might be given a material status of (dark or bright) "energy"? It should then be part of the content of the right-hand side of the Einstein equations. The purpose of this paper is to analyze some of the arguments in favor of each one of these interpretations of the cosmological constant. Recent estimates based on observational data give a bound on the graviton mass to be about 100 Mpc-1. If this value and the current estimate on the cosmological constant Λ are put into perspective, one faces the interesting coincidence that between the Compton wavelength of the graviton and the cosmological constant there exists the relation [Formula: see text]. Since a physical quantity like mass originates in a minkowskian conservation law, we proceed with a group theoretical interpretation of this relation in terms of the two possible Λ-deformations of the Poincaré group, namely the de Sitter and anti de Sitter groups. We use a very suitable formula, the so-called Garidi mass, and the typically dS/AdS dimensionless parameter ℏH/mc2 in order to make clear the asymptotic relations between minkowskian masses m and their possible dS/AdS counterparts. We conclude that if the fundamental state of the geometry of space-time is minkowskian, then the square of the mass of the graviton is proportional to Λ; otherwise, if the fundamental state is de Sitter, then the graviton is massless in the deSitterian sense.