Matter Sourced Bubble Nucleation in the Asymmetron Scalar-Tensor Theory

TL;DR

This work shows that matter-density distributions can catalyze bubble nucleation in the asymmetron scalar-tensor theory beyond traditional bulk Coleman–Callan nucleation. By introducing explicit symmetry breaking, the authors derive a density-tunable potential with true and false vacua, and they extend the instanton formalism to include boundary contributions from dense substrates using a Nambu–Goto-like action. They demonstrate that boundary effects generate a surface tension, leading to edge nucleation channels that, in many regimes (notably concave edges and small/curved substrates), have lower Euclidean action than bulk bubbles. The results illuminate how voids and dense objects influence domain formation in cosmology and in laboratory experiments, and they provide quantitative tools to compare edge versus bulk decay rates across planar, cylindrical, and curved geometries. The study thus broadens the phenomenology of false-vacuum decay in density-coupled scalar theories and suggests observable implications for cosmic voids, N-body simulations, and vacuum-chamber tests of fifth forces.

Abstract

We investigate how matter density distributions affect thin-wall bubble formation in the asymmetron mechanism, a scalar-tensor theory with a universal coupling to matter and explicit symmetry-breaking, and analyse the stability of its metastable state. We show that the screening mechanism of the asymmetron inside dense objects induces a surface tension associated with the boundary of the screening object, leading to a richer class of bubble solutions than the standard Coleman-Callan bulk nucleation. These boundary surface tensions are used to modify the Nambu-Goto action for instantons, allowing for the computation of the corresponding Euclidean action for bubbles nucleating on flat planes, as well as on concave and convex cylindrical surfaces. We find that the smallest Euclidean action occurs for bubbles nucleating along the edge of a concave spherical surface. Comparing this edge nucleation channel with the bulk one, we determine the maximum curvature radius for which concave edge nucleation is preferred. Since the maximum radius of curvature is exponentially suppressed by the action of a bulk bubble, we find that within the regime of the instanton approximation, edge nucleation is always preferred. This is largely due to the weak couplings of the asymmetron. We apply these findings to determine the maximum curvature radius of a cosmic void and discuss how our results affect the seeding of $N$-body simulations of asymmetron domains, showing that domain wall nucleation preferentially occurs at the edges of cosmological voids. We also demonstrate that the presence of a homogeneous gas around the dense substrates reduces the maximum curvature radius, enabling bulk bubbles to form preferentially as the asymmetron undergoes a density-driven phase transition.

Figures (9)

• Figure 1: On the left, we show the symmetron effective potential from Eq. (\ref{['effective-potential']}). On the right, we show the asymmetron effective potential Eq. (\ref{['effective-asymmeton-potential']}) with parameter choices $(\lambda, \kappa) = (1,0.05)$. In both cases, it is observed that for densities $\rho < \mu^2M^2$, the potentials exhibit symmetry breaking and have two minima. We show the potential at the critical density $\rho = \mu^2M^2$, where it can be seen that the potentials acquire a single minimum. For densities larger than $\rho>\mu^2 M^2$, the potentials have a single global minimum. However, the asymmetron potential exhibits explicit symmetry breaking as the degeneracy-breaking in the potential in the right-hand figure is clear. For both potentials, we have rescaled the scalar field by the VEV of the bare potential, $\phi_0$, which allows us to factorise out some of the parameter dependence of the potential, leading to the prefactor, $\lambda\phi_0^4$, by which we scale $V_\text{eff}(\phi)$. In the symmetron case, this makes the potential only dependent on the local matter density $\rho$. In the case of the asymmetron, however, the ratio $\kappa/\lambda$ contributes to the size of the explicit symmetry-breaking of the minima.
• Figure 3: Numerical plots of the true (left) and false (right) vacuum field profiles for several values of $R_s$ with $\kappa=0.01\lambda$ and $\rho_s=10\mu^2M^2$. $L_0=(\sqrt{2\mu})^{-1}$ is the symmetron Compton wavelength. The scalar field, $\phi$, is normalised in terms of the magnitude of the VEV of the bare symmetron potential, $\phi_0$. We use the variable $r$ because we are solving the full radial equation found in Eq. (\ref{['spherically-symmetric']}).
• Figure 4: $\Delta\sigma$ versus sphere radius $R_s$ (for $\kappa = 0.01\lambda$ and $\rho_s=10\rho_*$) shows a plateau at large $R_s$. The red-dashed line shows the planar-limit value of $\Delta\sigma$ derived in Eq. (\ref{['junction-condition']}).
• Figure 5: The spherical domain wall coupled to a dense matter sphere with radius $R_s$ (for $\kappa = 0.2\lambda$ and $\rho_s=50\rho_*$).
• Figure 6: A plot showing the functional dependence of $\frac{\Gamma(\rho)}{\Gamma(0)}$ with $\rho$ ($\kappa=0.9 \lambda$). For $\rho\simeq 0$, $\frac{\Gamma(\rho)}{\Gamma(0)}\sim \mathcal{O}(1)$ and a calculated value of $B_{0} = 547.55\hbar$. For an increasing density, $\frac{\Gamma(\rho)}{\Gamma(0)}$ increases rapidly. As the density is increased beyond $\rho\simeq 0.1\mu^2M^2$, the gradient of the ratio begins to decrease, until a maximum ratio is reached which occurs at a peak density, $\rho_\text{peak}\approx 0.98\rho_*$. Increasing the density beyond $\rho_\text{peak}$ results in a sharp drop-off, suppressing the rate of vacuum bubble production.