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

TL;DR

This paper critically examines the interpretations of the cosmological constant $\Lambda$ and explores its implications for the mass of the graviton, concluding that the graviton's mass depends on the fundamental geometry of spacetime.

Contribution

It presents a comparative analysis of the two main interpretations of $\Lambda$ and discusses their implications for the graviton's mass in different spacetime geometries.

Findings

If spacetime is Minkowskian, graviton mass squared is proportional to $\Lambda$.

If spacetime is de Sitter/Anti-de Sitter, the graviton is massless in the de Sitter sense.

The interpretation of $\Lambda$ influences the theoretical mass of the graviton.

Abstract

The existence of a non-zero cosmological constant $\Lambda$ gives rise to controversial interpretations. Is $\Lambda$ 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 $g\_{\mu\nu}$ 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 $\Lambda$, 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 $\Lambda$; otherwise, if the fundamental state is deSitter/AdS, then the graviton is massless in the deSitterian sense.