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 TI, 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 TI of the latter were less than 2TI (and for an approximately right-angled intersection if it were less than √ (2TI) which cannot occur in the class considered here. In an extensive category of multicomponent scalar field models of forced harmonic (linear or nonlinear) 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 Φi using a positive definite (Riemannian) energy metric dU2=G-tildeijdΦi that is obtained from the usual kinetic metric (which is flat for a model with an 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 characterized 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