Cosmological constraints on a dynamical electron mass

Motivated by recent astrophysical observations of quasar absorption systems, we formulate a simple theory where the electron to proton mass ratio $\mu =m_e/m_p$ is allowed to vary in spacetime. In such a minimal theory only the electron mass varies, with $\alpha$ and $m_p$ kept constant. We find that changes in $\mu$ will be driven by the electronic energy density after the electron mass threshold is crossed. Particle production in this scenario is negligible. The cosmological constraints imposed by recent astronomical observations are very weak, due to the low mass density in electrons. Unlike in similar theories for spacetime variation of the fine structure constant, the observational constraints on variations in $\mu$ imposed by the weak equivalence principle are much more stringent constraints than those from quasar spectra. Any time variation in the electron-proton mass ratio must be less than one part in ${10}^9$ since redshifts $z\approx 1$. This is more than 1000 times smaller than current spectroscopic sensitivities can achieve. Astronomically observable variations in the electron-proton must therefore arise directly from effects induced by varying fine structure “constant” or by processes associated with internal proton structure. We also place a new upper bound of $2\times {10}^{-8}$ on any large-scale spatial variation of $\mu$ that is compatible with the isotropy of the microwave background radiation. It is of course possible to bypass these constraints with the addition of a suitable potential to the dynamics.