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 will analyse the question of a Λ-dependent graviton mass, more precisely the possibility that between the Compton wavelength of the graviton and the cosmological constant there is the relation l g Λ 1 2 ≈ 1. Since a 1 physical quantity like mass originates in a minkowskian conservation law, we proceed to 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 H/mc 2 in order to make clear the asymptotic relations between minkowskian masses m and their possible dS/AdS counterparts. 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.

Constraint on reconstructed f(R) gravity models from gravitational waves

“…This stems from the sign mistakes of the linearized gravity Ricci tensor and the scalar curvature in that literature. Our second solution for the massive graviton is consistent with a tachyonic graviton of the de Sitter space shown in [2]. A massless graviton in the de Sitter space seems to appear as a tachyonic particle in Minkowski space.…”

One-loop renormalization of a gravity-scalar system

“…Although the use of the "massive" propagator is technically motivated, it may have deeper physical meanings. As stated in footnote 6, one implication is the possibility proposed in [40]. Another implication is for the renormalization procedure.…”

“…Treating the quadratic term arising from expansion of the cosmological constant term as the graviton "mass" term is motivated for a purely technically reason just stated; we do not mean that it is the genuine graviton mass term. It appears in the literature [40], however, that it is perhaps more than a technicality. Viewing the quadratic term as the graviton "mass" term has a further implication, mixing of physical states and unstable state, as we will comment on in section 3.…”

First-Order Cosmological Perturbations Engendered by Point-Like Masses

“…However, one should act with proper circumspection when discussing the massive graviton (see reasoning by Faraoni & Cooperstock (1998) as well as argumentation by Gazeau & Novello (2011) with respect to Minkowski and de Sitter spacetimes). It is remarkable that setting λ equal to /(m g c), ≡ h/(2π), gives m g = /(λc) ≈ 1.7×10 −33 eV today (when a = a 0 ), and the ratio 1/λ 2 = m 2 g c 2 / 2 turns out to be numerically equal to 2Λ/3.…”