Gravitational wave decay into dark energy

We study the decay of gravitational waves into dark energy fluctuations π, through the processes γ → ππ and γ → γ π, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator ½ ̃ m₄²(t) δ g⁰⁰ ( ⁽³⁾R + δ K_μ^ν δ K^μ_ν −δ K² ), so that the recent observations force ̃ m₄ = 0 (or equivalently 0α_H=). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to ̃ m₄² generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on ̃ m₄² comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable \hbox{higher-derivative corrections.}