Massless graviton in de Sitter as second sound in two-fluid hydrodynamics

TL;DR

This work addresses the unclear graviton mass spectrum in de Sitter spacetime by modeling the de Sitter vacuum as a two-fluid system with a normal component (gravitational degrees of freedom) and a superfluid component (dark energy). It identifies a second-sound–like entropy wave, governed by the normal component linked to the scalar curvature $R$, that propagates at the speed of light, $s_2=c$, under relations such as $T=H/π$ and $S=(3π T)/(4G)$, and shows that this mode can be viewed as a massless graviton analogue in de Sitter. The analysis uses the second-sound formula $s_2^2 = TS^2/(C_V ρ) · (ρ_s/ρ_n)$ with ρ=ρ_n+ρ_s=2ρ_n, C_V = S, and ρ_s = ρ_n, leading to s_2=c. The results offer a thermodynamic perspective on gravitons in de Sitter and motivate further exploration of the mode's precise gravitational interpretation, potential Goldstone-like nature, and implications for the cosmological constant problem.

Abstract

The concept of gravitons and their masses, clear in the case of Minkowski spacetime, remains ambiguous for de Sitter spacetime. Here, we used a two-fluid approach to de Sitter thermodynamics and found a collective mode that is analogous to second sound in the two-fluid dynamics of the de Sitter state. This mode is massless and propagates at the speed of light. This suggests that this second-sound analog is a massless graviton propagating in de Sitter spacetime. The type of graviton this mode represents requires further consideration.