Gravitational Waves from Feebly Interacting Particles in a First Order Phase Transition

TL;DR

This paper identifies feebly interacting particles (FIPs) as a novel channel for gravitational-wave production during a first-order phase transition, where most latent energy is carried by noninteracting particles that free-stream rather than forming a plasma. It develops a sprinkler formalism to compute the gravitational-wave spectrum from these free-streaming shells, finding a broader, distinctive spectrum with a peak near $k\approx0.77\beta$ and amplitudes comparable to standard sound-wave signals. The work provides a compact analytic fit to estimate the signal across dark-sector temperatures and degrees of freedom, highlighting observability with upcoming GW detectors over a wide range of energy scales. Overall, it demonstrates a realistic and efficient new GW source in dark-sector FOPTs that could help distinguish new physics in the early Universe.

Abstract

First order phase transitions are well-motivated and extensively studied sources of gravitational waves (GWs) from the early Universe. The vacuum energy released during such transitions is assumed to be transferred primarily either to the expanding bubble walls, whose collisions source GWs, or to the surrounding plasma, producing sound waves and turbulence, which source GWs. In this Letter, we study an alternative possibility that has not yet been considered: the released energy gets transferred primarily to feebly interacting particles that do not form a coherent interacting plasma but simply free-stream individually. We develop the formalism to study the production of GWs from such configurations, and demonstrate that such GW signals have qualitatively distinct characteristics compared to conventional sources and are potentially observable with near-future GW detectors.

Figures (8)

• Figure 1: Energy-momentum profile of particles inside an expanding bubble. The solid (dashed) curves denote $T_{\parallel}$ ($T_{\perp}$).
• Figure 2: Snapshots of time evolution of $(T_{ij} T_{ij})^{1/4}$ in the FIP scenario (BM1) (top), contrasted with an analogous simulation in the interacting scenario (SWs) Jinno:2020eqg (bottom). These plots are for illustrative purposes only, to highlight the qualitative differences between the two cases. Blue$\to$green$\to$yellow$\to$red (normalized differently for the two cases) denotes increasing $(T_{ij} T_{ij})^{1/4}$; the red dots in the top row are numerical artifacts.
• Figure 3: Gravitational wave spectrum obtained from simulations with 50 nucleation histories, rescaled as $\Omega^*_{\rm GW}/[(\bar{K}^{(\rm GW)})^2 (\frac{1}{24}m^2 T^2/\rho_{\rm tot})^2 (H/\beta)^2$]. The dashed black curve shows the broken power law fit $s/(1+s^3)$. The error bars correspond to the variance associated with the average over propagation directions. We have checked that the variance due to the different nucleation histories is significantly smaller.
• Figure 4: Absolute value of $\bar{K}^{\rm(GW)}$ as a function of $\gamma_w$ for $m/T = (1,2,3,4,5)$ (top to bottom). The black dashed curve is a numerical fit with formula $\bar{K}^{\rm(GW)} \sim 1 - 3/\gamma_w^{0.86}$. The black squares represent our BM points.
• Figure 5: Gravitational wave signals from FIPs with $m/T=3$, $v_w = 0.99$, and $g_*^D=5$ (which determine $\alpha = 0.23$). The different curves correspond to $T=5~{\rm TeV}, ~\beta/H = 100$ (blue), $T=5~{\rm TeV},~\beta/H = 50$ (red), $T=1~{\rm PeV},~\beta/H = 100$ (yellow), and $T=100~{\rm PeV},~\beta/H = 50$ (green). For comparison, we also show a sound wave signal (solid curve), using the same PT parameters as the blue curve, and $\alpha = 0.23$. The power-law integrated sensitivity curves for GW experiments Harry:2006fiKawamura:2006upPunturo:2010zz2017arXiv170200786AReitze:2019iox are for 1 year observation time, with signal-to-noise ratio $=1$, obtained from Schmitz:2020syl.