Stability of winding cosmic wall lattices with X type junctions

This work confirms the stability of a class of domain wall lattice models that can produce accelerated cosmological expansion, with pressure to density ratio w = −1/3 at early times, and with w = −2/3 at late times when the lattice scale becomes large compared to the wall thickness. For walls of tension T I, the relevant X type junctions could be unstable (for a sufficiently acute intersection angle α) against separation into a pair of Y type junctions joined by a compound wall, only if the tension T II of the latter were less than 2T I (and for an approximately right-angled intersection if it were less that √ 2T I) which can not occur in the class considered here. In an extensive category of multicomponent scalar field models of forced harmonic (linear or non-linear) type it is shown how the relevant tension – which is the same as the surface energy density U of the wall – can be calculated as the minimum (geodesic) distance between the relevant vacuum states as measured on the space of field values Φ using a positive definite (Riemannian) energy metric dU 2 = G̃ij dΦ i dΦ that is obtained from the usual kinetic metric (which is flat for a model with ordinary linear kinetic part) by application of a conformal factor proportional to the relevant potential function V . For suitably periodic potential functions there will be corresponding periodic configurations – with parallel walls characterised by incrementation of a winding number – in which the condition for stability of large scale bunching modes is shown to be satisfied automatically. It is suggested that such a configuration – with a lattice lengthscale comparable to intergalactic separation distances – might have been produced by a late stage of cosmological inflation.