String-induced vacuum decay

TL;DR

The paper analyzes false vacuum decay catalyzed by cosmic strings, revealing an $O(2)\times O(2)$ symmetric bounce that seeds true-vacuum bubbles along a string, potentially erasing the string network. Using a minimal complex scalar with a sextic potential under a $U(1)$ symmetry, the authors develop a fully relativistic thin-wall treatment for both global and local strings, deriving explicit bounce actions and identifying parameter regions where string-induced decay dominates over the standard $O(4)$ channel. They compute the bubble quadrupole moment and discuss novel GW sources from non-spherical bubble expansion and transient string networks, showing that metastability can suppress or alter the GW spectrum in ways that may intersect with PTA observations. A concrete two-field realization is presented to generate the string network and its delayed decay, with implications for early-unary cosmology and potential connections to the Hubble tension via new early dark energy frameworks. Overall, the work provides a tractable mechanism by which cosmic strings can catalyze vacuum decay and produce distinctive gravitational-wave signatures, motivating further nonperturbative analyses and phenomenological explorations.

Abstract

False vacuum decay typically proceeds via the nucleation of spherical bubbles of true vacuum, described by $O(4)$ symmetric field configurations in Euclidean time. In this work, we investigate how the presence of cosmic strings can catalyze the decay process. To this end, we consider a complex scalar field charged under a global or local $U(1)$ symmetry. Assuming a non-trivial vacuum manifold, realizable for example in a simple sextic potential, we derive relativistic bounce solutions with $O(2) \times O(2)$ symmetry, corresponding to elongated bubbles seeded by a cosmic string of the same scalar field. Building up on earlier results in the literature, we identify the region of parameter space where vacuum decay predominantly proceeds via this alternative channel, thereby providing an explicit mechanism for the quantum decay of cosmic strings. Finally, we present an initial discussion of the gravitational wave signal associated with this type of vacuum decay and its possible connection to the recently observed stochastic signal in pulsar timing arrays.

Figures (8)

• Figure 1: Schematic illustration of the Coleman $O(4)$ bounce (left), and the $O(2)\times O(2)$ bounce in the presence of a cosmic string (right).
• Figure 2: Sketch of the potential in Eq. \ref{['eq:V2']}. For $\epsilon<0$, the true vacuum lies at $|\phi| = v_f/\sqrt{2}$ and the system admits stable cosmic strings (dashed line). In this work, we focus on the case $\epsilon > 0$, where the true vacuum is at $\phi = 0$, rendering the cosmic string metastable (solid line).
• Figure 3: Radial profiles $R(\varrho)$ of the bounce solution for global (left) and local (right) strings with three values of the parameter $x$ or $y$ (solid lines). For $x,y \ll 1$, the profile converges to the $O(4)$-symmetric solution $\sqrt{\mathcal{R}_c^2 - \varrho^2}$, with $\mathcal{R}_c = 3\sigma/\Delta V$, which represents the Coleman bounce in the absence of strings and is shown as the gray curve. The dashed curves depicts the analytic continuation of each profile to $\varrho\to -\,i\varrho$, describing the late post-phase transition evolution of the bubble wall. All quantities are plotted in units of $\sigma/\Delta V$.
• Figure 4: Numerical bounce results for the global (black) and local (blue) string obtained from a shooting algorithm as functions of $x$ and $y$, respectively. The dots represent the numerical shooting result and the solid lines correspond to the semi-analytic fitting functions in \ref{['eq:semi-analytic']} and \ref{['eq:semi-analytic_local']}. The quantities in both plots are normalized with respect to the Coleman bounce and thus approach unity as $x\rightarrow 0$. Left: The normalized bounce action $b(\cdot)=B(\cdot)/B_0$ (solid). The dotted lines depict the 'non-relativistic approximation', which fails to recover the Coleman limit for the global string but is reliable for $x \to 1$. Right: The bounce radius evaluated at the bubble center at initial time $R(\varrho=0; \cdot)/\mathcal{R}_c$ (solid) and the metastable string radius $R_s(\cdot)/\mathcal{R}_c$ as defined in \ref{['eq:metastable_string']} (dashed). For $x,y \to 1$ both quantities approach each other.
• Figure 5: The regularized quadrupole moment $Q^\mathrm{(reg)}$ in units of $\Delta V R^5(t)$, as a function of the radius $R(t)$ for a single $O(2) \times O(2)$ bubble. The same quantity is vanishing for spherical bubbles nucleated in the absence of a cosmic string.