© 2018 American Physical Society. Adopting the Landau-Lifshiftz method of classical fluctuations, we determine the statistical average strength of the fluctuations of the energy flux on the apparent horizon of a homogeneous and isotropic universe described by Einstein gravity. We find that the fluctuations increase with the temperature of the horizon and decrease with its area, in accordance with the features of systems where gravity can be neglected. We further find, on the one hand, that the fluctuations vanish in the cosmological constant dominated de Sitter expansion and, on the other hand, that the domination of phantom fields is excluded. The reasonableness of the results we have obtained lend support to the view that the Universe behaves as a normal thermodynamic system.