Gravitational waves from an axion-dark photon system: A lattice study

Abstract

In this work, we present a lattice study of an axion - dark photon system in the early Universe and show that the stochastic gravitational wave (GW) background produced by this system may be probed by future GW experiments across a vast range of frequencies. The numerical simulation on the lattice allows us to take into account non-linear backreaction effects and enables us to accurately predict the final relic abundance of the axion or axion-like particle (ALP) as well as its inhomogeneities, and gives a more precise prediction of the GW spectrum. Importantly, we find that the GW spectrum has more power at high momenta due to 2\rightarrow12→1 processes. Furthermore, we find the degree of polarization of the peak of the GW spectrum depends on the ALP-dark photon coupling and that the polarization can be washed out or even flipped for large values thereof. In line with recent results in the literature, we find the ALP relic abundance may be suppressed by two orders of magnitude and discuss possible extensions of the model that expand the viable parameter space. Finally, we discuss the possibility to probe ultralight ALP dark matter via spectral distortions of the CMB.

Gravitational waves and dark photon dark matter from axion rotations

“…It decreases in proportion to f 3 for frequency f < f GW [63], and is sharply cut off above f GW . The scattering of the dark photon and the axion will make the spectrum broader [21,23]. The scattering is expected to be more efficient than the case of axion oscillations as we will discuss in section 4.…”

“…Determining the precise spectrum of the dark photons requires a numerical lattice simulation beyond the scope of this paper. Motivated by the detailed study of tachyonic instability in other contexts [21,23], we assume that when H = H p , the momentum distribution of dark photons is sharply peaked at k TI and the dark photon energy density is as large as the energy stored in the rotations at the onset of the tachyonic instability, ρ θ .…”

“…The possibility of dark photon dark radiation from tachyonic instability is also discussed in refs. [17,18,23]. In the (nearly) massless case, the contribution to N eff is intimately tied to the size of the GW signal.…”

“…(3.7). Without a detailed lattice simulation dedicated to the case of an axion with rotation, such as the one done in the non-rotating case [23], one cannot more precisely determine the relative energy transferred from the rotation to the GWs and the dark photon. For larger GW signals, a more precise computation could be of interest to establish a firm prediction for CMB-S4 [64].…”

“…The produced dark photons are highly inhomogeneous and source gravitational waves [18,19]. This scenario was recently considered to explain the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) signal [20], but it was found that the axion oscillation leads to an excessive amount of dark matter [21] unless the axion mass decreases after the beginning of the oscillations [22,23]. The produced dark photons may be dark matter [24][25][26].…”