## Wednesday, July 31, 2013

### Planck's summer: varying electron masses

fifth post by Youness in the "Planck's summer"-series:

How can we test whether the electron mass changes with time (as compared to the other particle masses)? Give a list of astrophysical or cosmological observations that are sensitive to the electron mass (from the early to the late Universe). Do you have an idea how to measure the present time variation of the electron mass in the lab?

*Answer: In cosmology and astrophysics, a natural idea is to look at spectral lines. For the hydrogen atom, you certainly remember $E_n \propto m_e$; or, more precisely, the energy levels are proportional to the reduced mass $m_e m_p / (m_e + m_p)$. Spectral lines of stars and quasars already contain a lot of information about the time evolution of $m_e$. Furthermore, the CMB is due to the recombination into the hydrogen ground state; thereby, the time when the CMB has formed is also sensitive to $E_1 \propto m_e$. Going back further, to nucleosynthesis, I think the electron mass will be important for the phase space volume accessible to reactions. For example, the phase space of the $\beta$ decay of the neutron, $n \to p + e^- + {\bar \nu}_e$ depends on the electron mass. Even further in the past there was a moment when the temperature of the primordial plasma fell below $2 m_e$, i.e. when electrons and positrons eventually annihilated. This process heats up the photons (as compared to the already decoupled neutrinos) leading to the famous factor of $(11/4)^{1/3}$. I guess the precise value, however, will depend on the electron mass but I'm not sure whether the effect would be big enough to be observable. On the other hand, we can at least infer that the epoch of electron-positron annihilation took place after neutrino decoupling (otherwise, the temperatures of the photons and the neutrinos would be equal, which means that the photon temperature would be reduced as compared to the standard calculation). This gives an upper limit on the electron mass.