We investigate cosmology of massive electrodynamics and explore the possibility whether massive photon could provide an explanation of the dark energy. The action is given by the scalar-vector-tensor theory of gravity which is obtained by non-minimal coupling of the massive Stueckelberg QED with gravity and its cosmological consequences are studied by paying a particular attention to the role of photon mass. We find that the theory allows cosmological evolution where the radiation- and matter-dominated epochs are followed by a long period of virtually constant dark energy that closely mimics $Lambda$CDM model and the main source of the current acceleration is provided by the nonvanishing photon mass governed by the relation $Lambdasim m^2$. A detailed numerical analysis shows that the nonvanishing photon mass of the order of $sim 10^{-34}$ eV is consistent with the current observations. This magnitude is far less than the most stringent limit on the photon mass available so far, which is of the order of $m leq 10^{-27}$eV.
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