Effect of time variation in the Higgs vacuum expectation value on the cosmic microwave background

Abstract

A time variation in the Higgs vacuum expectation value alters the electron mass and thereby changes the ionization history of the universe. This change produces a measurable imprint on the pattern of cosmic microwave background (CMB) fluctuations. The nuclear masses and nuclear binding energies, as well as the Fermi coupling constant, are also altered, with negligible impact on the CMB. We calculate the changes in the spectrum of the CMB fluctuations as a function of the change in the electron mass ${m}_{e}.$ We find that future CMB experiments could be sensitive to $|\ensuremath{\Delta}{m}_{e}{/m}_{e}|\ensuremath{\sim}|\ensuremath{\Delta}{G}_{F}{/G}_{F}|\ensuremath{\sim}{10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}.$ However, we also show that a change in ${m}_{e}$ is nearly, but not exactly, degenerate with a change in the fine-structure constant $\ensuremath{\alpha}.$ If both ${m}_{e}$ and $\ensuremath{\alpha}$ are time varying, the corresponding CMB limits are much weaker, particularly for $l<1000.$