Cosmological Evolution of Fundamental Constants: From Theory to   Experiment
  In this paper we discuss a possible cosmological time evolution of fundamental constants from the theoretical and experimental point of views. On the theoretical side, we explain that such a cosmological time evolution is actually something very natural which can be described by mechanisms similar to those used to explain cosmic inflation. We then discuss implications for grand unified theories, showing that the unification condition of the gauge coupling could evolve with cosmological time. Measurements of the electron-to-proton mass ratio can test grand unified theories using low energy data. Following the theoretical discussion, we review the current status of precision measurements of fundamental constants and their potential cosmological time dependence. 
Xavier Calmet and Matthias Keller
gr-qc astro-ph.CO physics.atom-ph quant-ph