Observational Constraints on Varying-alpha Domain Walls

We consider the possibility that current hints of spatial variations of the fine structure constant at high redshift, based on VLT/UVES and Keck/HIRES observations, could be caused by a biased domain wall network described by a scalar field non-minimally coupled to the electromagnetic field. We show that in order to be responsible for the reported spatial variations of the fine structure constant, the fractional contribution of the domain wall network to the energy density of the Universe should be tightly constrained within the range $10^{-10} < \Omega_{w0} < 10^{-5}$. We also show that the domain wall dynamics should be essentially frictionless, so that its characteristic scale is in the order of the Hubble radius at the present time.