|Foam. Image source: DoITPoMS.|
The best visualization that came to my mind is a foam-like structure that fills the universe, though you shouldn't take this comparison too seriously.
At the domain walls, the axion field has to change values in order to interpolate between the different domains. This position-dependence of the field however creates a contribution to the energy density. Since the energy density of the domain walls decays slower with the expansion of the universe than the energy density of ordinary matter, this can become problematic, in the sense that it's in conflict with observation.
There are various ways to adjust these models or to pick the parameter ranges so that the domain walls do not appear to begin with, decay quickly, or are unlikely to be present in our observable universe. These are the most commonly used strategies for those interested in the axion as a particle. But in the recent years there has also been an increasing interest in using the domain walls themselves as gravitational sources, and so it has been suggested that they might play the role of dark energy or make contributions to dark matter.
In an interesting paper that appeared recently in PRL, Pospelov et al lay out how we could measure if planet Earth passed through such a domain wall
- How do you know if you ran through a wall?
M. Pospelov, S. Pustelny, M. P. Ledbetter, D. F. Jackson Kimball, W. Gawlik, D. Budker
Phys. Rev. Lett. 110, 021803 (2013)
The idea is to use the coupling of the gradient of the axion field, which is non-zero at the domain walls, to the spin of particles of the standard model. A passing through the domain wall would oh-so-slightly change the orientation of spins and align them into one direction.
This could be measured with devices normally used for very sensitive measurements of magnetic fields, optical magnetometers. Optical magnetometers consist basically of a bunch of atoms in gaseous form, typically alkali metals with one electron in the outer shell. These atoms are pumped with light into a polarized state of higher angular momentum, and then their polarization is measured again with light. This measurement is very sensitive to any change to the atomic spin's orientation, which may be caused by magnetic fields - or domain walls.
In the paper, and in a more recent follow-up paper, they estimate that that presently existing technology can test interesting parameter ranges of the model when other known constraints (mostly astrophysical) on the coupling of the axion have been taken into account. It should be mentioned though that they consider not a pure QCD axion, but a general axion-like field, in which case the relation between the mass of the particle and its coupling is not fixed.
The sensitivity to the event of a domain wall passing can be increased by not only reading out one particular magnetometer, but by monitoring many of them at the same time. Then one can look for correlations between them. This way one is not only able to better pick out a signal from the noise, but from the correlation time one could also determine the velocity of the passing through the domain wall.
I think this is an interesting experiment that nicely complements existing searches for dark matter. I also like it for its generality. Maybe while searching for axion domain walls, we'll find something else that we're moving through and that happens to couple very weakly to spins.