Non-Scaling Topological Defects and Gravitational Waves in Higgs Portal

TL;DR

This work addresses whether topological defects can form in Higgs portal dark sectors without conventional symmetry restoration. Using analytic arguments and lattice simulations, it shows that a negative thermal mass and non-adiabatic oscillations of the dark Higgs drive the field through the origin and trigger tachyonic growth, seeding domain walls or cosmic strings. The resulting defects possess large tensions at formation, emitting gravitational waves with a peak at $k_{\rm peak} \sim (a H)|_{T_{\rm osc}}$, consistent with standard defect-network expectations. These findings imply potentially observable gravitational waves and related structures such as miniclusters or primordial black holes, offering new probes of Higgs portal physics and early-Universe dynamics.

Abstract

One of the simplest extensions of the Standard Model is the Higgs portal extension involving a dark Higgs. Dark sectors that include dark matter candidates, WIMPs, axions, and dark photons, can naturally have this type of interaction, where the dark Higgs is charged under some symmetry, which may or may not be spontaneous broken by the vacuum expectation value. In this paper, using lattice simulations, I show that if the reheating temperature of the Universe is sufficiently high, topological defects such as domain walls and cosmic strings associated with these symmetries are naturally formed even if the symmetries are never restored due to negative thermal mass squareds. This occurs due to the early Universe's non-adiabatic oscillation of the Higgs around the onset of oscillation, which overshoots the origin, and tachyonic instability that enhances fluctuations. The gravitational waves generated by these topological defects may be very significant due to the energetic processes induced by matter effects in the hot and dense Universe irrelevant to the typical energy scale of the dark sector in the vacuum or whether the symmetry is broken in the vacuum. Alongside earlier studies such as usual phase transition, melting domain walls and melting cosmic strings scenarios that assume a symmetric phase in the early Universe, the Higgs portal models naturally predict local overdensities from topological defects, which may induce miniclusters and primordial black holes, as well as the gravitational waves.These phenomena provide novel opportunities to search for such scenarios. I also perform various numerical simulations for the relevant topic including melting domain walls and cosmic strings with inflationary and Gaussian fluctuations, for comparison--which have not been performed previously.

Figures (21)

• Figure 1: Solution of the field equation without fluctuations. Here, $\phi$ multiplied by the scale factor $a$ is plotted against varying scale factor which is normalized to be unity at the beginning. Several initial conditions in the radiation-dominated era with negative thermal mass squared are used. The dashed lines denote $a |\phi|$ when $\phi$ is positive, while solid lines denote the same quantity when $\phi$ is negative. See the main text for the setup of the calculation.
• Figure 2: Snapshot of the lattice simulation at $\tau=101d^{-1}$. The top panels (blue contours) represent the case for the $Z_2$ symmetric potential, while the lower panels represent the $U(1)$ case. The left panels have Gaussian initial fluctuations, while the right panels have scale-invariant fluctuations. Here, $\bar{\Phi} \neq 0$ as the initial fluctuation.
• Figure 3: Time evolution of the GW spectra. Each panel corresponds to those in Fig. \ref{['fig:2']}. The time evolution is taken from $\tau=1d^{-1}$ to $\tau=231d^{-1}$, with the plots shown from lighter to darker for each panel.
• Figure 4: Snapshot of $Z_2$ models with Gaussian fluctuations at $\tau = 151/d$.
• Figure 5: GW spectra from $Z_2$ models with Gaussian fluctuations.