Gravitational wave oscillations in Multi-Proca dark energy models

TL;DR

This paper investigates gravitational wave oscillations in Multi-Proca dark energy models, analyzing their theoretical properties, potential detectability, and implications for current and future gravitational wave observations.

Contribution

It provides a detailed analysis of gravitational wave oscillations in Multi-Proca models, including background solutions and the impact on gravitational wave signals, highlighting the challenges in detecting such effects.

Findings

Oscillations are present but require a mass scale much larger than the Hubble constant.

Detectability of oscillations is unlikely in these models due to mass scale constraints.

Gravitational wave oscillations cannot explain signals if detected at frequencies associated with ultra-light dark energy masses.

Abstract

Gravitational wave oscillations arise from the exchange of energy between the metric perturbations and additional tensor modes. This phenomenon can occur even when the extra degrees of freedom consist of a triplet of massive Abelian vector fields, as in Multi-Proca dark energy models. In this work, we study gravitational wave oscillations in this class of models minimally coupled to gravity with a general potential, allowing also for a kinetic coupling between the vector field and dark matter that can, in principle, enhance the modulation of gravitational wave amplitudes. After consistently solving the background dynamics, requiring the model parameters to reproduce a phase of late-time accelerated expansion, we assess the accuracy of commonly used analytical approximations and quantify the impact of gravitational wave amplitude modulation for current detectors (LIGO--Virgo) and future missions such as LISA. Although oscillations are present in these scenarios, we find that the effective mass scale (the mixing mass) governing the phenomenon is $m_g \sim \mu_A$, where $\mu_A$ is the (time-dependent) effective mass of the vector dark-energy field. Detectability of gravitational wave oscillations, however, requires $m_g \gg H_0$, which is in tension with the ultra-light masses typically needed to drive accelerated expansion $\mu_A \sim H_0 \sim 10^{-33}\,\mathrm{eV}$. Therefore, if gravitational wave oscillations were to be detected at the corresponding frequencies, they could not be attributed to these classes of dark-energy models.