Biased domain walls: faster annihilation, weaker gravitational waves

Abstract We study the evolution of domain wall networks and their phenomenological implications in a model of a real scalar χ , where a Z 2 -symmetry is slightly broken by a potential bias V bias . It is demonstrated that the latter triggers domain wall annihilation considerably earlier than previously thought. Namely, we observe that the scaling relation t ann ∝ 1/ V bias 2/3 for the annihilation time t ann fits to the simulation data better than a commonly assumed t ann ∝ 1/ V bias . As a result, the energy density of gravitational waves produced by the network of biased domain walls, for a given tiny V bias , is suppressed compared to naive expectations. The spectral shape of gravitational waves is similar to that resulting from unbiased domain walls, but with more power in the close-to-maximum ultraviolet part. In the far ultraviolet region, the spectrum of gravitational waves becomes nearly flat; such a plateau has been recognised earlier in the case of unbiased walls. In our investigation we mainly focus on the symmetry breaking potential V breaking ∝ χ 3 , and argue that no significant modifications of the domain walls evolution take place if one includes higher powers of χ .