Time variation of the fine structure constant and of the Higgs vacuum expectation value on cosmological time scales

Abstract

Aims. We study the time variation of both the fine structure constant, α, and the Higgs vacuum expectation value, v, during Big Bang nucleosynthesis (BBN). Methods. We calculate the primordial abundances of D, 4He, and 7Li by modifying Kawano's code, and by using observational data we set constraints on the joint variation of α and v. To perform the calculations we considered the dependence of the deuterium-binding energy, D, upon v, obtained from the treatment of different proton-neutron interactions. Results. Results are consistent with variation on v (even at the level of 6σ) and null variation of α (within 2σ) if the 7Li data are used in the analysis. However, if data on these nuclei are not considered in the statistical analysis, we found null variation on both fundamental constants within 2σ. Conclusions. We found that the best-fit values of the variation of v and α are sensible to the dependence of the deuterium binding energy upon the Higgs vacuum expectation value. We found non-null variation of v within 6σ if all the observational data are used in the analysis. If data on the primordial abundance of 7Li are taken at face value, the discrepancy between BBN and WMAP estimates may be explained by allowing variations of v.