Varying Alpha in a More Realistic Universe

Abstract

We study the space-time evolution of the fine structure constant, $α$, inside evolving spherical overdensities in a lambda-CDM Friedmann universe using the spherical infall model. We show that its value inside virialised regions will be significantly larger than in the low-density background universe. The consideration of the inhomogeneous evolution of the universe is therefore essential for a correct comparison of extragalactic and solar system limits on, and observations of, possible time variation in $α$ and other constants. Time variation in $α$ in the cosmological background can give rise to no locally observable variations inside virialised overdensities like the one in which we live, explaining the discrepancy between astrophysical and geochemical observations.

Figures (5)

• Figure 1: Evolution of $\alpha$ in the background (dashed line) and inside clusters (solid lines) as a function of $\log (1+z)$. Initial conditions were set to match observations of $\alpha$ variation in ref. murphy. Two clusters virialise at different redshifts, one of them in order to have $\alpha _{c}(z_{v}=1)=\alpha _{0}$. Vertical lines represent the moment of turn-around.
• Figure 2: Evolution of $\Delta \alpha /\alpha$ in the background (dashed lines) and inside clusters (solid lines) as a function of $\log (1+z)$. Initial conditions were set to match observations of $\alpha$ variation in ref. murphy. Four clusters that virialised at different redshifts. All clusters were started so as to have $\alpha _{c}(z_{v})=\alpha _{0}$.
• Figure 3: Plot of $\alpha$ as a function of $\log (1+z_v)$, at virialisation. Clusters (solid line), background (dashed line).
• Figure 4: Plot of $\Delta \alpha/ \alpha$ as a function of $\log (1+z_v)$, at virialisation. Clusters (solid line), background (dashed line).
• Figure 5: Variation of $\delta \alpha /\alpha$ with $\delta \rho /\rho$ at the cluster virialisation redshift. The evolution of $\alpha$ inside the clusters was normalised to satisfy the latest time-variation observational results, and to have $\alpha _{c}(z_{v})=\alpha _{0}$ for ${z}_{v}{=1.}$