Where are the walls? Spatial variation in the fine-structure constant

The reported spatial variation in the fine structure constant at high redshift, if physical, could be due to the presence of dilatonic domains, and one or more domain walls inside our horizon. An absorption spectrum of an object in a different domain from our own would be characterized by a different value of α. We show that while a single-wall solution is statically comparable to a dipole fit, and is a big improvement over a weighted mean (despite adding three parameters), a two-wall solution is a far better fit (despite adding three parameters over the single-wall solution). We derive a simple model accounting for the two domain wall solution. The goodness of these fits is, however, dependent on the extra random error which was argued to account for the large scatter in most of the data. When this error is omitted, all the above solutions are poor fits to the data. When included, the solutions that exhibit a spatial dependence agree with the data much more significantly than the standard model; however, the standard model itself is not a terrible fit to the data, having a p value of ∼20%.