A New Source of Phase Transition Gravitational Waves: Heavy Particle Braking Across Bubble Walls

TL;DR

This paper introduces a novel microscopic source of gravitational waves produced when heavy particles brake as they cross expanding bubble walls during a cosmological first-order phase transition. The authors develop a quantum-field-theoretic treatment of graviton bremsstrahlung in the wall background, deriving the emission probability and the resulting GW energy density and spectrum, including redshift to today. The spectrum exhibits a peak linked to the bubble-wall velocity and a mass-dependent amplitude that scales as $m^4$, with a possible double-peak structure for $m\lesssim T$; heavy beyond-Standard-Model states thus imprint distinctive high-frequency signals. The mechanism is illustrated in a scale-invariant $B-L$ model, where bubble dynamics, wall velocity, and reheating are analyzed and linked to observable GW features, suggesting a new avenue to probe heavy particle dynamics and high-frequency gravitational waves.

Abstract

Motivated by the new heavy dark matter production mechanism from cosmic phase transition, we propose a novel mechanism for the generation of microscopic gravitational waves (GWs) during cosmological first-order phase transitions arising from the braking of heavy particles as they traverse bubble walls. Unlike the well-known sources such as bubble collisions, sound waves, or turbulence in the plasma, this mechanism originates from the direct interaction between massive particles and the expanding bubble wall. We use quantum field theory to rigorously compute the gravitational radiation. The resulting GW spectrum exhibits distinctive features: The peak frequency is tightly correlated with the bubble wall velocity, while the peak amplitude scales as the fourth power of the heavy particle mass. These unique dependencies offer a new observational handle on particle physics beyond the Standard Model. We illustrate this mechanism within a specific model framework and demonstrate its viability. Our findings enrich the landscape of phase transition GW sources and open new avenues for more directly probing heavy particle dynamics and new physics models in the early universe.

Figures (7)

• Figure 1: Schematic illustration of a scalar particle crossing the bubble wall during a first-order phase transition. As it enters the true vacuum region, the particle acquires mass and emits a graviton via bremsstrahlung. In the upper left corner of the figure, the selection of the coordinate axes is marked. In the wall frame, the direction of motion of the incident particle is taken to be along the positive $z$-axis. Relatively, from the perspective of the plasma frame, the bubble wall moves towards the particles along the negative $z$-axis. We denote by $v_w$ and $L_w$ the velocity and width of the bubble wall, respectively.
• Figure 2: Integration region in the $p_a^z$–$\tilde{E}_k$ plane. The orange line corresponds to $p_a^z = 4\gamma \tilde{E}_k$, while the green line denotes $p_a^z = 4\gamma \tilde{E}_k - 4\gamma^2 L_w^{-1}$. The six distinct regions share a common boundary point at $(\gamma L_w^{-1},\, 4\gamma^2 L_w^{-1})$.
• Figure 3: GW spectra generated by heavy particles traversing bubble walls during a first-order phase transition. The parameters $m$, $T$, $L_w$, and $\gamma$ are treated as free inputs. We fix the vacuum expectation value to $v_{\phi} = 10^{13}~\mathrm{GeV}$ and the bubble wall Lorentz factor to $\gamma = 10^6$. Spectra are shown for three representative cases: $v_{\phi}/T = 10$, $50$, and $100$. Other parameters are estimated as $m = v_{\phi}$ and $L_w = 1/T$. The infinite series part of the function $I_{\rm low}$ is evaluated using its first 100 terms, which are sufficient to ensure numerical convergence.
• Figure 4: GW spectra generated by heavy particles interacting with bubble walls during a first-order phase transition. The parameters $m$, $v_\phi$, $L_w$, and $\gamma$ are treated as free inputs. We fix the temperature at $T = 10^{11}~\mathrm{GeV}$ and the bubble wall Lorentz factor at $\gamma = 10^6$. The figure illustrates three representative cases with $v_\phi/T = 10$, $50$, and $100$. Other parameters are estimated as $m = v_\phi$ and $L_w = 1/T$. The infinite series part of the function $I_{\rm low}$ is evaluated using its first 100 terms, which are sufficient to ensure numerical convergence.
• Figure 5: GW spectra generated by heavy particles interacting with bubble walls during a first-order phase transition. The parameters $m$, $v_\phi$, $L_w$, and $\gamma$ are treated as free inputs. We fix the temperature at $T = 10^{12}~\mathrm{GeV}$ and the bubble wall Lorentz factor at $\gamma = 10^6$. The figure illustrates three representative cases with $m/T = 0.1$, $1$, and $10$. The bubble wall thickness is estimated as $L_w = 1/T$. The infinite series part of the function $I_{\rm low}$ is evaluated using its first 100 terms, which are sufficient to ensure numerical convergence.