The nature of $Λ$ and the mass of the graviton: A critical view

Abstract

The existence of a non-zero cosmological constant $Λ$ gives rise to controversial interpretations. 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 perturbative calculus performed on the metric $g\_{μν}$ 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 not to elucidate the fundamental nature of $Λ$, but instead we aim to present and discuss some of the arguments in favor of both interpretations of the cosmological constant. We conclude that if the fundamental 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 deSitter/AdS, then the graviton is massless in the deSitterian sense.