Wall of fundamental constants

We consider the signatures of a domain wall produced in the spontaneous symmetry breaking involving a dilatonlike scalar field coupled to electromagnetism. Domains on either side of the wall exhibit slight differences in their respective values of the fine-structure constant, $\alpha$. If such a wall is present within our Hubble volume, absorption spectra at large redshifts may or may not provide a variation in $\alpha$ relative to the terrestrial value, depending on our relative position with respect to the wall. This wall could resolve the contradiction between claims of a variation of $\alpha$ based on Keck/Hires data and of the constancy of $\alpha$ based on Very Large Telescope data. We derive the properties of the wall and the parameters of the underlying microscopic model required to reproduce the possible spatial variation of $\alpha$. We discuss the constraints on the existence of the low-energy domain wall and describe its observational implications concerning the variation of the fundamental constants.

Figure 1

(a) A domain wall is assumed to cross our Hubble volume. It intersects our past-light-cone on a 2-dimensional spatial hypersurface characterized by the redshift of the wall in a direction $\mathbf{n}$, $z_W(\mathbf{n})$. $z_{*}$ is the lowest redshift at which the wall can be observed and corresponds to a direction ${\mathbf{n}}_{*}$. According to Ref. 16, ${\mathbf{n}}_{*}$ should point towards right ascension $17.3\pm 0.6$ hours and declination $-61\pm 9\mathrm{deg}$. (b) On a constant time hypersurface, the wall crosses our Hubble horizon so that the fine-structure constant takes 2 values: ${\alpha }_{+}$ in our neighborhood and ${\alpha }_{-}$ on the other side of the wall.

Figure 2

Evolution of the physical velocity of the wall $v$ (solid line) and of the associated boost factor $\gamma$ (dotted line), plotted as a function of cosmological redshift $z$. We recall that time evolves from right to left in the Figure.

Figure 3

Summary of the observable prediction of our model. Assuming the wall is at a redshift $z_{*}\sim 1.8$ at its closest position to us in a direction ${\mathbf{n}}_{*}$, then the fine-structure constant is a function of $\cos \theta ={\mathbf{n}}_{*}·\mathbf{n}$ and $z$. The dark (blue) region corresponds to $\alpha ={\alpha }_{-}$ and the upper region to $\alpha ={\alpha }_{+}$. The fact that our observable universe has a finite radius implies that we shall detect no variation for angles larger than ${\theta }_l$.