TIME VARIATION OF THE FINE STRUCTURE CONSTANT IN THE SPACETIME OF A COSMIC DOMAIN WALL

The gravitational field produced by a domain wall acts as a medium with spacetime-dependent permittivity ε. Therefore, the fine structure constant α=e2/4πε will be a time-dependent function at fixed position. The most stringent constraint on the time-variation of α comes from the natural reactor Oklo and gives [Formula: see text]. This limit constrains the tension of a cosmic domain wall to be less than σ ≲ 10-2 MeV 3, and then represents the most severe limit on the energy density of a cosmic wall stretching our Universe.