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 a) 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 v 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 i using a positive definite ( Riemannian) energy metric dU2 = Gij d i d j 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.