Effects of spontaneous Z₂ symmetry breaking or restoration in Gauss–Bonnet gravity

This work presents a comprehensive investigation of the formation and cosmological implications of domain walls within the framework of Einstein–Gauss–Bonnet (EGB) gravity. A pivotal feature of this model is the capacity for the scalar field Lagrangian to undergo a spontaneous process of Z₂ symmetry breaking and restoration. This phase transition is a fundamental prerequisite for the formation of topological defects, specifically domain walls, which arise as solitonic solutions interpolating between the distinct vacua of the theory. We perform a detailed numerical analysis of the dynamics of a neutral scalar field non-minimally coupled to the Gauss–Bonnet invariant, exploring its behavior across different cosmological backgrounds. Our findings demonstrate that the coupling to the Gauss–Bonnet term facilitates the formation of the static domain wall in terms of proper distance in a de Sitter (inflationary) background. Furthermore, we extend our analysis to a radiation-dominated epoch, where we identify that expansion leads to the "melting" of these walls. To assess the potential observational signatures of this scenario, we calculate the predicted spectrum of stochastic gravitational waves generated by the network dynamics using the CosmoLattice package. Additionally, we study the production of primordial black holes, which could be associated with the collapse of domain wall structures. Regrettably, our calculations indicate that the direct observational detection of such domain walls from this model lies beyond the reach of foreseeable experiments.