Black Writing, White Reading

On the cosmological domain wall problem for the minimally extended supersymmetric standard model

“…In comparison to the cases shown in Ref. [13], we see that the wall is thinner and the surface energy higher, as expected. We note that if both A k and A λ are zero, then the Z 3 symmetry of the scalar potential becomes a U(1) symmetry, and so the wall energy falls to zero and its width becomes infinite; in this limit however we have an axion problem.…”

“…Eventually pressure dominates as expected and the entire volume is cleared of walls. This contrasts with the no-pressure case, where one or two horizon-sized walls always remain [13]. The behaviour for different values of the pressure or surface tension is identical if the time and length, respectively, are scaled appropriately.…”

“…The structure of these walls may be determined by finding time-independent solutions to the classical field equations after imposing the boundary conditions that at the endpoints the fields should be in distinct vacuum configurations. This has been done using numerical methods for the NMSSM potential [13] and we reiterate the essential features of the Z 3 walls. As might be expected from dimensional arguments and by analogy with the analytically soluble case of a single real scalar field in a Z 2 symmetric potential [9], the thickness and energy density of the walls are of order ν −1 and ν 3 respectively, where ν is a typical vacuum expectation value.…”

“…We show this happening in Figure 3, where we have performed a simple thin wall simulation of a network of domain walls using techniques similar to those used in ref. [18], and which we have discussed in more detail elsewhere [13]. In the absence of friction it is convenient to rescale the parameters with some typical length scale, R 0 , which we choose to be 1 cm, corresponding approximately to the curvature scale when pressure becomes dominant if ε ∼ M 5 W /M Pl .…”