Dynamical Prevention of Topological Defect Formation

TL;DR

The paper tackles the problem of post-inflationary topological defect formation by showing that a symmetry-breaking scalar can remain in a broken phase if it dynamically tracks a time-dependent minimum induced by a negative Hubble mass, or by negative thermal/non-thermal mass terms generated via couplings to a light scalar $\chi$. It combines analytical tracking conditions with numerical simulations across chaotic and new inflation backgrounds, and analyzes both thermalized and non-equilibrium (preheating) scenarios. The key results establish criteria under which the field avoids zero-crossing, such as $\sigma_{\rm min} = \left( c H^2 / \lambda_n \right)^{1/(n-2)}$ and $n>6$ (matter) or $n>10$ (radiation); in the renormalizable case $n=4$, coupling to $\chi$ can still prevent crossing, with thermal or preheating-induced masses providing the mechanism. The findings have broad implications for PQ scalars in axion models and more generally for GUTs, discrete symmetries, and NMSSM-like theories, offering a dynamical route to defect-free cosmologies and potentially relaxing isocurvature constraints by keeping the field value large during inflation.

Abstract

Topological defects can have significant cosmological consequences, so their production must be examined carefully. It is usually assumed that topological defects are produced if the temperature becomes sufficiently high, but in reality their formation depends on the post-inflationary dynamics of a symmetry-breaking scalar. We analyze the dynamics of a symmetry-breaking scalar field in the early universe within models that provide an effective negative mass term at the origin, and show that the symmetry can remain broken so that topological defects are never formed. In particular, we demonstrate that nonthermally produced particles (such as the Standard Model Higgs) during preheating can generate such an effective negative mass term, allowing the scalar field to follow a time-dependent minimum even in renormalizable models with a quartic coupling. We also discuss the implications of this result for the Peccei-Quinn scalar in axion models.

Figures (10)

• Figure 1: The time evolution of the inflaton field (left) and the Hubble parameter (right) in the chaotic inflation model. The dashed line in the left panel corresponds to the negative $\phi$.
• Figure 2: The numerical results of the motion of $\sigma$ (colored lines) normalized by $\sigma_0$ in the chaotic inflation model. Each panel shows a different $n$ case, and the colors of lines differ by the coupling constant $c$. The gray lines show the time evolution of $\sigma_{\rm min}$, the potential minimum, which is also normalized by $\sigma_0$. We fix the self-coupling constant of $\sigma$ by $\lambda_n = m_\phi^{4-n}$ for $n = 6,8$. Since the quartic coupling constant can be scaled out through a field redefinition, $\sigma \rightarrow \sqrt{\lambda_4} \sigma$, in the classical level, $\sigma(t) / \sigma_0$ does not depend on $\lambda_4$.
• Figure 3: The time evolution of the inflaton field (left) and the Hubble parameter (right) in the new inflation model (\ref{['eq:NewInf']}) for $\ell=6$ and $v=M_{\rm pl}$. The time is normalized by the Hubble parameter during inflation, $H_{\rm inf}$.
• Figure 4: Same as Fig. \ref{['fig: sigmaHM']} but for the new inflation model (\ref{['eq:NewInf']}). The time is normalized by the Hubble parameter during inflation, $H_{\rm inf}$.
• Figure 5: The numerical results of the evolution of $\sigma$ (blue lines) in the thermal case. The horizontal axis represents the scale factor $a$ normalized to the initial value $a_{\rm in}$. The right panel shows a close-up of the left panel. The gray lines show the time evolution of $\sigma_{\rm min}$. The vertical line in the left panel denotes $H = H_{\rm R}$. We used $c = 1$, $\lambda_{\chi \sigma} = 0.5$, $\lambda_4 = 0.3$, $H_\mathrm{inf} = 10^9$ GeV, and $T_{\rm R} = 10^{12}$ GeV.