Spatial variations of the fine-structure constant in symmetron models

Abstract

We investigate the variation of the fine-structure constant, $\ensuremath{\alpha}$, in symmetron models using N-body simulations in which the full spatial distribution of $\ensuremath{\alpha}$ at different redshifts has been calculated. In particular, we obtain simulated sky maps for this variation, and determine its power spectrum. We find that in high-density regions of space (such as deep inside dark matter halos) the value of $\ensuremath{\alpha}$ approaches the value measured on Earth. In the low-density outskirts of halos the scalar field value can approach the symmetry breaking value and leads to significantly different values of $\ensuremath{\alpha}$. If the scalar-photon coupling strength ${\ensuremath{\beta}}_{\ensuremath{\gamma}}$ is of order unity we find that the variation of $\ensuremath{\alpha}$ inside dark matter halos can be of the same magnitude as the recent claims by Webb et al. of a dipole variation. Importantly, our results also show that with low-redshift symmetry breaking these models exhibit some dependence of $\ensuremath{\alpha}$ on lookback time (as opposed to a pure spatial dipole) which could in principle be detected by sufficiently accurate spectroscopic measurements, such as those of ALMA and the ELT-HIRES.