Stability of winding cosmic wall lattices with X type junctions

Abstract

Abstract. 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 √ 2 T 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 i using a positive definite (Riemannian) energy metric dU 2 =G ij dΦ i dΦ j 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 distancesmight have been produced by a late stage of cosmological inflation.

The role of domain wall junctions in Carter's pentahedral model

“…Carter's pentahedral model has a potential given by [10,13] where Φ = |Φ| e iφ , Ψ = |Ψ| e iψ , 0 < < 1, V = V 0 , θ = 2φ + ψ and χ = 2ψ − φ. The potential has five minima with V = 0 satisfying cos θ = cos χ = −1 and |Φ| 2 = |Ψ| 2 = 1/(1 − ).…”

“…Carter's pentahedral model [10,13] has been constructed as an example of a model having an odd number of vacuum configurations giving rise to an even type system through the formation of X-type junctions. However, in [5,6] the claim that Carter's pentahedral model would form X-type junctions has been challenged and it was argued that Y-type junctions would be formed instead.…”

Effect of kinematic constraints on multitension string network evolution

“…Studies of the collisions of Nambu-Goto strings with junctions at which three strings meet have shown that the exchange to form junctions cannot occur if the strings meet with very large relative velocity. For the case of non-Abelian strings, rather than passing through one another they become stuck in an X configuration [34,36], in each case the constraint depending on the angle at which the strings meet, on their relative velocity, and on the ratios of the string tensions. Calculations of the average speed at which a junction moves along each of the three strings from which it is formed yield results consistent with the observation that junction dynamics may be such as to preferentially remove the heavy strings from the network leaving a network of predominantly light strings.…”

Impact of string and monopole-type junctions on domain wall dynamics: Implications for dark energy

“…We use the energy density fractions as weight factors in the estimate of the Hubble damping term which needs to be added to Eq. (7). The equation describing the evolution of the characteristic velocity of the network then becomes…”