H.A. Wilson, then R.H. Dicke, proposed to describe gravitation by a spatial change of the refractive index of the vacuum around a gravitational mass. Dicke extended this formalism in order to describe the apparent expansion of the universe by a cosmological time dependence of the global vacuum index. In this paper, we develop Dicke’s formalism. The metric expansion in standard cosmology (the time-dependent scale factor of the Friedmann–Lemaître curved spacetime metric) is replaced by a flat and static Euclidean metric with a change with time of the vacuum index. We show that a vacuum index increasing with time produces both the cosmological redshift and time dilation, and that the predicted evolution of the energy density of the cosmological microwave background is consistent with the standard cosmology. We then show that the type Ia supernovæ data, from the joint SDSS-II and SNLS SNe-Ia samples, are well modeled by a vacuum index varying exponentially as $n(t)=exp(t/\tau _0)$ , where $\tau _0=8.0^{+0.2-0.8}$  Gyr. The main consequence of this formalism is that the cosmological redshift should affect any atom, with a relative decrease of the energy levels of about $-2 \ 10^{-18} \ \mathrm {s}^{-1}$ . Possibilities for an experimental investigation of this prediction are discussed.