Gravitational Wave Mountains: current-carrying domain walls

TL;DR

Domain walls from discrete-symmetry breaking can generate GWs when they annihilate, but current-carrying DWs with trapped fermions introduce a metastable spheron object that imprints a secondary GW peak. The authors develop a semi-analytic framework for such DWs, deriving the spheron radius $R_\text{sph}$ by balancing wall tension against fermion-induced centrifugal energy, and compute the GW spectrum including a fission-driven peak; they also present numerical support for spheron formation. The results show that the spheron-induced peak can be sizable and fall within LISA/ET sensitivity for realistic parameter choices, offering a distinctive signature to distinguish BSM scenarios with DW currents from standard DW backgrounds. This signature enhances the prospects for early-Universe probes of new physics, while motivating lattice simulations and cross-checks with PTA and CMB constraints to map the viable parameter space.

Abstract

Domain wall (DW) networks may have formed in the early universe following the spontaneous breaking of a discrete symmetry. Notably, several particle physics models predict the existence of current-carrying DWs, which can capture and store particles as zero modes on it. In this study, we demonstrate that gravitational waves (GWs) generated by current-carrying DWs with fermionic zeromodes exhibit a novel feature: an additional peak in the GW spectrum resembling mountains, arising from metastable topological remnants, which we term ``spherons.'' This distinct signature could be detectable in upcoming GW observatories such as LISA and ET. The results suggest that DW networks in beyond Standard Model scenarios could emit GW signals that are significantly stronger and with greater detectability than previously expected.

Figures (8)

• Figure 1: The time evolution of the radius $R_\mathrm{sol}$ of the decaying spheron in the case of charge leakage, which is obtained by solving Eq. \ref{['eq:effectiveEOM']}. We here took a dimensionless unit $\sigma^{1/3}=1$ and $G=10^{-6}$. The cutoff $R_\mathrm{cutoff}$ is a radius at which the trapped fermions can escape to the bulk, leading to classical instability of the spheron, which is calculated by $m_\psi=10\, \sigma^{1/3}$. $R_\mathrm{sch}$ is the Schwarzchild radius.
• Figure 2: Schematic illustration of the spheron decaying by the fission. Right after the fission, the two smaller spherons are significantly deviated from the spherical shape and can radiate GW to be relaxed.
• Figure 3: GW spectrum from DW network and spheron. In each figure, thick solid curves indicate superposition of those from the conventional DW network (left peaks) and from the spherons which are decaying due to the fission (right peaks).
• Figure 4: Parameter space where the two GW signals will be observed with $\mathrm{SNR} > 10$ (upper-right side of the contours) for different GW experiments. We separate the calculation into the signals from the spherons (solid contours) and the conventional DW network (DWN) (dashed lines). The black star indicates the benchmark point corresponding to the blue curve in the left panel in Fig. \ref{['fig:GW-spectrum-sph']}. The gray bottom-right region is excluded due to the DW domination (Eq. \ref{['eq:V-cond']}) while in the purple right-bottom region the network annihilation is later than the spheron lifetime so that the spheron cannot be formed.
• Figure 5: GW spectrum from DW network and spheron. We took the parameters $\sigma$ and $\Delta V$ such that the GW spectrum from the network fits recent PTA signals (NANOGrav: gray, EPTA: red). If one fixes $T_\mathrm{dec}=2\, \mathrm{MeV}$, the additional peak from spherons can lie within LISA sensitivity range (purple) for $10^{-12}\lesssim Y \lesssim 10^{-9}$.