A phenomenological model is proposed to explain the recent observed cosmological variation of the fine structure constant as an effect of the quantum vacuum , assuming a flat universe with cosmological constant \Lambda in the cases ( \Omega _ { M } , \Omega _ { \Lambda } ) equal to ( 0.3 , 0.7 ) and ( 1 , 0 ) .
Because of the fourth Heisenberg relation , the lifetime of the virtual pairs of the zero-point radiation must depend on the gravitational potential \Phi , so that the quantum vacuum changes its density and acquires a relative permittivity different from one .
Since the matter was more concentrated in the past , the gravitational potential of all the universe was stronger and the optical density of the vacuum higher , the electron charge being therefore more renormalized and smaller than now .
The model is based on a first order Newtonian approximation that is valid for the range of the observations , but not for very high redshift , the prediction being that \Delta \alpha / \alpha is proportional to \ { \Omega _ { M } [ a ( t ) ^ { -1 } -1 ] -2 \Omega _ { \Lambda } [ a ( t ) ^ { 2 } -1 ] \ } , a ( t ) being the scale factor .
This agrees with the observations .