Unifying cosmological and recent time variations of fundamental couplings

A number of positive and null results on the time variation of fundamental constants have been reported. It is difficult to judge whether or not these claims are mutually consistent, since the observable quantities depend on several parameters, namely, the coupling strengths and masses of particles. The evolution of these coupling-parameters over cosmological history is also a priori unknown. A direct comparison requires a relation between the couplings. We explore several distinct scenarios based on unification of gauge couplings, providing a representative (though not exhaustive) sample of such relations. For each scenario we obtain a characteristic time dependence and discuss whether a monotonic time evolution is allowed. For all scenarios, some contradictions between different observations appear. We show how a clear observational determination of nonzero variations would test the dominant mechanism of varying couplings within unified theories.

Figure 1

Variations for varying $\alpha$ alone. Only observations constraining $\alpha$ variation are shown; the BBN fit including ${}^7\mathrm{Li}$ is poor (${\chi }^2/\nu \ge 7.8/2$) hence we also display a conservative bound from ${}^4\mathrm{He}$ and D abundances neglecting ${}^7\mathrm{Li}$.

Figure 2

Variations for scenario 2; BBN bounds are $2\sigma$ bounds.

Figure 3

Variations for scenario 3; BBN bounds are $2\sigma$. Note that due to the very large ratio $\Delta \ln \mu /\Delta \ln \alpha$ in this scenario, points indicating any nonzero variation of $\alpha$ fall well outside the range of the graph.

Figure 4

Variations for scenario 4; BBN bounds are $2\sigma$.

Figure 5

Variations for scenario 5, $\tilde{\gamma }=42$; BBN bounds are $2\sigma$.

Figure 6

Variations for scenario 6, $\tilde{\gamma }=70$; BBN bounds are $2\sigma$.

Figure 7

Variations for scenario 6, $\tilde{\gamma }=25$; BBN bounds are $2\sigma$.

Figure 8

Normalized evolution factors ${\overline{l}}_i/{\overline{l}}_4$ for each scenario, where ${\overline{l}}_i\equiv l_i/\ln (1+z_i)$.