We investigated domain wall networks as a possible candidate to explain the present accelerated expansion of the universe. We discuss various requirements that any stable lattice of frustrated walls must obey and propose a class of `ideal' model (regarding its potential to lead to network frustration). By using the results of the largest and most accurate three-dimensional field theory simulations of domain wall networks with junctions, we find compelling evidence for a gradual approach to scaling. We conjecture that, even though one can build (by hand) lattices that would be stable, no such lattices will ever come out of realistic domain wall forming cosmological phase transitions. 
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We consider cosmic strings and magnetic monopoles in Bekenstein-type models and show that there is a class of models of this type for which the classical Nielsen-Olesen vortex and 't Hooft-Polyakov monopoles are still valid solutions. We show that Equivalence Principle constraints impose tight limits on the allowed variations of α induced by string networks on cosmological scales. We show that the results obtained using the spherical infall model for an infinite wavelength inhomogeneity are inconsistent with the results of a local linearised gravity study, and we argue in favour of the second approach. We also criticise the claim that the value of α inside collapsed regions could be significantly different from the background one by these findings.

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