Gravitational Wave Decay into Dark Energy

TL;DR

This paper investigates how gravitational waves decay into dark energy fluctuations within the EFT framework, deriving constraints on theory parameters from observational data and analyzing loop effects on graviton propagation.

Contribution

It identifies the decay process constraints on EFT operators, ruling out certain theories, and examines loop-induced modifications to graviton dispersion relations.

Findings

Decay processes constrain EFT parameters, especially $ ilde m_4$.

Recent observations force $ ilde m_4=0$, excluding some theories.

Loop corrections induce non-Lorentz invariant graviton dispersion modifications.

Abstract

We study the decay of gravitational waves into dark energy fluctuations $\pi$, through the processes $\gamma \to \pi\pi$ and $\gamma \to \gamma \pi$, 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 $\frac12 \tilde m_4^2(t) \, \delta g^{00}\, \left( {}^{(3)}\! R + \delta K_\mu^\nu \delta K^\mu_\nu -\delta K^2 \right)$, so that the recent observations force $\tilde m_4 =0$ (or equivalently $\alpha_{\rm H}=0$). 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 $\tilde m_4^2$ generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on $\tilde m_4^2$ comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable higher-derivative corrections.