Cosmic domain walls on a lattice: illusive effects of initial conditions

Abstract

Evolution of cosmic domain walls (DWs) settles to the scaling solution, which is often assumed to be independent of initial conditions. However, lattice simulations performed in this work reveal a clear dependence of the scaling DW area on the initial configuration of the sourcing scalar field, specifically, its infrared (IR) properties. Namely, the DW area grows as one suppresses IR modes in the initial scalar field spectrum. This growth is saturated, when the area parameter $\xi$ commonly used in the literature reaches the value $\xi_{max} \approx 1.2$. The dependence of $\xi$ on IR modes is argued to be of non-physical origin: it is likely to be due to effects of the lattice boundary. Assuming that physically the memory of initial conditions is erased, one recognizes $\xi \approx 1.2$ obtained in the situation with maximally suppressed IR modes as a genuine universal value of the area parameter in the scaling regime. We demonstrate that ignorance about initial conditions may affect predictions for the energy density of gravitational waves by the factor five. The spectral shape of gravitational waves is also affected by the choice of initial conditions, most notably in the low-frequency part. Likewise, we revisit annihilation of DWs under the influence of a potential bias. It has been previously found in Ref. [19] that the annihilation happens significantly earlier compared to the estimate based on the simple balance between the potential bias and surface energy density. We further support this observation and show that the tendency towards an earlier annihilation gets even stronger upon removing IR modes in simulations.